Packing

2112 cases · 4 beaten · 464 reproduced · 1644 behind

Pack n unit items (circles, or regular polygons, tans, dominoes and L's allowed to rotate) in the smallest container: circle, triangle, square, pentagon, hexagon, octagon, tan, domino, or the L (a 2x2 square with one corner unit square removed; the page lists its long side). Validated with exact decimal predicates and no overlap tolerance; the beaten circle-in-L cases were also checked in exact rational arithmetic by two independently written checkers.

Beaten (4)

Circles in an L, n = 44

15.270195484 vs listed 15.27022+
margin +2.45e-05 (0.000%)

Found by Tej Stead in June 2026.

figure · coordinates

Circles in an L, n = 45

15.431836747 vs listed 15.43636+
margin +4.52e-03 (0.029%)

Found by Tej Stead in June 2026.

figure · coordinates

Circles in an L, n = 46

15.709648886 vs listed 15.71083+
margin +1.18e-03 (0.008%)

Found by Jonathan Viquerat in September 2026.

figure · coordinates

Hexagons in a domino, n = 5

3.248710331 vs listed 3.24871+
margin +9.75e-07 (0.000%)

Found by Jonathan Viquerat in April 2026.

figure · coordinates

All cases

showing cases

Problem	n	Listed on the page	Our certified value	Margin	Margin %	Status	Listed by
Circles in a circle	2	r = 2	2.000000001	−8.00e-10	-0.000	reproduced
Circles in a circle	3	r = 1 + 2 / √3 = 2.154+	2.154700539	−8.62e-10	-0.000	reproduced
Circles in a circle	4	r = 1 + √2 = 2.414+	2.414213563	−9.66e-10	-0.000	reproduced
Circles in a circle	12	r = 4.029+	4.029601932	−6.02e-04	-0.015	reproduced	Found by Kravitz in 1967.
Circles in a circle	14	r = 4.328+	4.328428557	−4.29e-04	-0.010	reproduced	Found by Goldberg in 1971.
Circles in a circle	15	r = 4.521+	4.521356967	−3.57e-04	-0.008	reproduced	Found by Kravitz in 1967.
Circles in a circle	16	r = 4.615+	4.615425597	−4.26e-04	-0.009	reproduced	Found by Goldberg in 1971.
Circles in a circle	17	r = 4.792+	4.792033750	−3.38e-05	-0.001	reproduced	Found by Reis in 1975.
Circles in a circle	18	r = 1 + √2 + √6 = 4.863+	4.863703307	−1.95e-09	-0.000	reproduced	Found by Kravitz in 1967.
Circles in a circle	20	r = 5.122+	5.122320739	−3.21e-04	-0.006	reproduced	Found by Goldberg in 1971.
Circles in a hexagon	2	s = 1 + 2/√3 = 2.154+	2.154700539	−8.62e-10	-0.000	reproduced
Circles in a hexagon	3	s = 4/√3 = 2.309+	2.309401078	−9.24e-10	-0.000	reproduced
Circles in a hexagon	4	s = 2/√3 + 4/√7 = 2.666+	2.666558431	−1.07e-09	-0.000	reproduced	Found by Shahriar Manzoor in April 2002.
Circles in a hexagon	5	s = 2.999+	2.999355401	−3.55e-04	-0.012	reproduced	Found by Erich Friedman in 1999.
Circles in a hexagon	6	s = 2 + 2/√3 = 3.154+	3.154700540	−1.26e-09	-0.000	reproduced
Circles in a hexagon	7	s = 2 + 2/√3 = 3.154+	3.154700540	−1.26e-09	-0.000	reproduced
Circles in a hexagon	8	s = 3.709+	3.709400096	−4.00e-04	-0.011	reproduced	Found by David W. Cantrell in July 2002.
Circles in a hexagon	9	s = 20/7 + 2/√3 = 4.011+	4.011843397	−1.60e-09	-0.000	reproduced	Found by David W. Cantrell in July 2002.
Circles in a hexagon	10	s = 4.119+	4.119357181	−3.57e-04	-0.009	reproduced	Found by David W. Cantrell in July 2002.
Circles in a hexagon	11	s = 2 + 4/√3 = 4.309+	4.309401078	−1.72e-09	-0.000	reproduced	Found by Erich Friedman in 1999.
Circles in a hexagon	12	s = 2 + 4/√3 = 4.309+	4.309401078	−1.72e-09	-0.000	reproduced	Found by Erich Friedman in 1999.
Circles in a hexagon	13	s = 8/√3 = 4.618+	4.618802155	−1.85e-09	-0.000	reproduced	Found by Erich Friedman in 1999.
Circles in a hexagon	14	s = 2 + 2/√3 + 4/√7 = 4.666+	4.666558432	−1.87e-09	-0.000	reproduced	Found by David W. Cantrell in July 2002.
Circles in a hexagon	15	s = 4.961+	4.961321279	−3.21e-04	-0.006	reproduced	Found by David W. Cantrell in January 2006.
Circles in a hexagon	16	s = 4.999+	4.999355401	−3.55e-04	-0.007	reproduced	Found by David W. Cantrell in July 2002.
Circles in a hexagon	17	s = 5.133+	5.133119426	−1.19e-04	-0.002	reproduced	Found by David W. Cantrell in January 2006.
Circles in a hexagon	18	s = 4 + 2/√3 = 5.154+	5.154700540	−1.55e-09	-0.000	reproduced
Circles in a hexagon	19	s = 4 + 2/√3 = 5.154+	5.154700540	−1.55e-09	-0.000	reproduced
Circles in a hexagon	20	s = 5.676+	5.676887318	−8.87e-04	-0.016	reproduced	Found by David W. Cantrell in July 2012.
Circles in a hexagon	21	s = 5.709+	5.709400097	−4.00e-04	-0.007	reproduced	Found by David W. Cantrell in July 2012.
Circles in a hexagon	22	s = 5.952+	5.951749794	+2.50e-04	0.004	reproduced	Found by David W. Cantrell in July 2012.
Circles in a hexagon	23	s = 34/7 + 2/√3 = 6.011+	6.011843397	−1.80e-09	-0.000	reproduced	Found by David W. Cantrell in July 2012.
Circles in a hexagon	24	s = 6.117+	6.117620861	−6.21e-04	-0.010	reproduced	Found by Rob Pratt in March 2020.
Circles in a pentagon	2	s = 2tan(36°) + √5 - 1 s = 2.689+	2.689153035	−1.53e-04	-0.006	reproduced
Circles in a pentagon	3	s = 3.015+	3.015862479	−8.62e-04	-0.029	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	4	s = 3.314+	3.314449566	−4.50e-04	-0.014	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	5	s = 2tan(36°) + 2 s = 3.453+	3.453085057	−8.51e-05	-0.002	reproduced
Circles in a pentagon	6	s = 2tan(36°) + 4sin(36°) s = 3.804+	3.804226067	−2.26e-04	-0.006	reproduced
Circles in a pentagon	7	s = 4.236+	4.236120738	−1.21e-04	-0.003	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	8	s = 4.564+	4.564580947	−5.81e-04	-0.013	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	9	s = 4.825+	4.825026360	−2.64e-05	-0.001	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	10	s = 5.095+	5.095192535	−1.93e-04	-0.004	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	11	s = 5.240+	5.240278496	−2.78e-04	-0.005	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	12	s = 5.407+	5.407790091	−7.90e-04	-0.015	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	13	s = 5.651+	5.651781418	−7.81e-04	-0.014	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	14	s = 5.808+	5.808533027	−5.33e-04	-0.009	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	15	s = 5.945+	5.945158606	−1.59e-04	-0.003	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	16	s = 6.129+	6.129607483	−6.07e-04	-0.010	reproduced	Found by George Sicherman in July 2012.
Circles in a pentagon	17	s = 6.419+	6.419436755	−4.37e-04	-0.007	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	18	s = 6.586+	6.586813631	−8.14e-04	-0.012	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	19	s = 6.777+	6.777892052	−8.92e-04	-0.013	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	20	s = 6.944+	6.944556888	−5.57e-04	-0.008	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	21	s = 7.107+	7.107266889	−2.67e-04	-0.004	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	22	s = 7.271+	7.271271706	−2.72e-04	-0.004	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	23	s = 7.397+	7.397090335	−9.03e-05	-0.001	reproduced	Found by David W. Cantrell in July 2012.
Circles in a pentagon	24	s = 7.534+	7.534389921	−3.90e-04	-0.005	reproduced	Found by David W. Cantrell in July 2012.
Circles in a square	2	s = 2 + √2 = 3.414+	3.414213564	−1.37e-09	-0.000	reproduced
Circles in a square	3	s = 2 + 1/√2 + √6/2 = 3.931+	3.931851654	−1.57e-09	-0.000	reproduced
Circles in a square	4	s = 4	4.000000002	−1.60e-09	-0.000	reproduced
Circles in a square	5	s = 2 + 2√2 = 4.828+	4.828427127	−1.93e-09	-0.000	reproduced
Circles in a tan	8	s = 2 + 3√2 + √6 = 8.692+	8.692130433	−3.48e-09	-0.000	reproduced	Found by Hans Melissen in 1997.
Circles in a tan	9	s = 2 + 5√2 = 9.071+	9.071067815	−3.63e-09	-0.000	reproduced
Circles in a tan	10	s = 8 + √2 = 9.414+	9.414213566	−3.77e-09	-0.000	reproduced
Circles in a tan	11	s = 5 + √(2/3) + 3√2 = 10.059+	10.059137272	−4.02e-09	-0.000	reproduced	Found by David W. Cantrell in June 2005.
Circles in a tan	12	s = 10.422+	10.422815211	−8.15e-04	-0.008	reproduced	Found by David W. Cantrell in June 2005.
Circles in a tan	13	s = 10.798+	10.798666393	−6.66e-04	-0.006	reproduced	Found by Hans Melissen in 1997.
Circles in a tan	14	s = 2 + 3√2 + 2√6 = 11.141+	11.141620177	−4.46e-09	-0.000	reproduced	Found by Erich Friedman in April 2005.
Circles in a tan	15	s = 10 + √2 = 11.414+	11.414213565	−3.02e-09	-0.000	reproduced
Circles in a tan	16	s = 11.892+	11.891982511	+1.75e-05	0.000	reproduced	Found by David W. Cantrell in January 2006.
Circles in a tan	17	s = 12.155+	12.155914064	−9.14e-04	-0.008	reproduced	Found by David W. Cantrell in January 2006.
Circles in a tan	18	s = 12.542+	12.542719624	−7.20e-04	-0.006	reproduced	Found by Eckard Specht in April 2009.
Circles in a tan	19	s = 12.798+	12.798666392	−6.66e-04	-0.005	reproduced	Found by David W. Cantrell in January 2006.
Circles in a tan	20	s = 13.092+	13.092605393	−6.05e-04	-0.005	reproduced	Found by Maurizio Morandi in December 2008.
Circles in a tan	21	s = 12 + √2 = 13.414+	13.414213566	−3.72e-09	-0.000	reproduced
Circles in a triangle	2	s = 2 + 2√3 = 5.464+	5.464101617	−2.19e-09	-0.000	reproduced
Circles in a triangle	3	s = 2 + 2√3 = 5.464+	5.464101617	−2.19e-09	-0.000	reproduced
Circles in a triangle	13	s = 4 + 2√6/3 + 10√3/3 = 11.406+	11.406495858	−4.56e-09	-0.000	reproduced	Found by Melissen in 1993.
Circles in a triangle	14	s = 8 + 2√3 = 11.464+	11.464101620	−4.59e-09	-0.000	reproduced	Found by Erdős/Oler in 1961.
Circles in an L	2	s = 4	4.000000002	−1.60e-09	-0.000	reproduced
Circles in an L	3	s = 4	4.000000002	−1.60e-09	-0.000	reproduced
Circles in an L	4	s = 5.304+	5.304812895	−8.13e-04	-0.015	reproduced	Found by Erich Friedman in June 2005.
Circles in an L	5	s = 5.780+	5.780892895	−8.93e-04	-0.015	reproduced	Found by David W. Cantrell in June 2005.
Circles in an L	6	s = 6.416+	6.416500412	−5.00e-04	-0.008	reproduced	Found by David W. Cantrell in June 2005.
Circles in an L	7	s = 6.787+	6.787322146	−3.22e-04	-0.005	reproduced	Found by David W. Cantrell in June 2005.
Circles in an L	8	s = 7.116+	7.116251345	−2.51e-04	-0.004	reproduced	Found by Erich Friedman in June 2005.
Circles in an L	9	s = 4 + 12/√13 = 7.328+	7.328201180	−2.93e-09	-0.000	reproduced	Found by Erich Friedman in June 2005.
Circles in an L	10	s = 7.628+	7.628290963	−2.91e-04	-0.004	reproduced	Found by Erich Friedman in June 2005.
Circles in an L	11	s = 4 + √2 + √6 = 7.863+	7.863703308	−3.15e-09	-0.000	reproduced	Found by David W. Cantrell in January 2006.
Circles in an L	12	s = 8	8.000000003	−3.20e-09	-0.000	reproduced
Circles in an L	13	s = 8.812+	8.812490023	−4.90e-04	-0.006	reproduced	Found by David W. Cantrell in January 2006.
Circles in an L	14	s = 9.085+	9.085893323	−8.93e-04	-0.010	reproduced	Found by David W. Cantrell in January 2006.
Circles in an L	15	s = 9.412+	9.412649498	−6.49e-04	-0.007	reproduced	Found by David W. Cantrell in January 2006.
Circles in an L	16	s = 9.635+	9.635745974	−7.46e-04	-0.008	reproduced	Found by David W. Cantrell in January 2006.
Circles in an L	17	s = 10.00425+	10.004253590	−3.59e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	18	s = 10.27388+	10.273885059	−5.06e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	19	s = 10.46489+	10.464896647	−6.65e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	20	s = 10.61664+	10.616645072	−5.07e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	21	s = 10.82564+	10.825649498	−9.50e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	22	s = 10.89927+	10.899275670	−5.67e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	23	s = 11.21781+	11.217812413	−2.41e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	24	s = 11.41224+	11.412241305	−1.30e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	25	s = 11.71270+	11.712699601	+3.99e-07	0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	26	s = 11.86038+	11.860386699	−6.70e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	27	s = 12	12.000000003	−3.28e-09	-0.000	reproduced
Circles in an L	28	s = 12.49680+	12.496806465	−6.46e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	29	s = 12.67553+	12.675529689	+3.11e-07	0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	30	s = 12.94284+	12.942845261	−5.26e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	31	s = 13.12408+	13.124080708	−7.08e-07	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	32	s = 13.30282+	13.302823642	−3.64e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	33	s = 13.52754+	13.527544221	−4.22e-06	-0.000	reproduced	Found by Jonathan Viquerat in September 2026.
Circles in an L	34	s = 13.72415+	13.724157861	−7.86e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	35	s = 13.86770+	13.867708776	−8.78e-06	-0.000	reproduced	Found by Leo Strijbos in August 2026.
Circles in an L	36	s = 14.01152+	14.011527575	−7.58e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	37	s = 14.10954+	14.109546337	−6.34e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	38	s = 14.23736+	14.237364434	−4.43e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	39	s = 14.30561+	14.305616537	−6.54e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	40	s = 14.54974+	14.549742882	−2.88e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	41	s = 14.69163+	14.691693600	−6.36e-05	-0.000	behind	Found by Tej Stead in June 2026.
Circles in an L	42	s = 14.90788+	14.907881852	−1.85e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	43	s = 15.06571+	15.065713308	−3.31e-06	-0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	44	s = 15.27022+	15.270195484	+2.45e-05	0.000	beaten	Found by Tej Stead in June 2026.
Circles in an L	45	s = 15.43636+	15.431836747	+4.52e-03	0.029	beaten	Found by Tej Stead in June 2026.
Circles in an L	46	s = 15.71083+	15.709648886	+1.18e-03	0.008	beaten	Found by Jonathan Viquerat in September 2026.
Circles in an L	47	s = 15.85935+	15.859349870	+1.30e-07	0.000	reproduced	Found by Jonathan Viquerat in September 2026.
Circles in an L	48	s = 15.98311+	15.983106863	+3.14e-06	0.000	reproduced	Found by Tej Stead in June 2026.
Circles in an L	49	s = 16.13179+	16.131792995	−3.00e-06	-0.000	reproduced	Found by Leo Strijbos in August 2026.
Circles in an L	50	s = 16.30078+	16.300776166	+3.83e-06	0.000	reproduced	Found by Jonathan Viquerat in September 2026.
Dominoes in a circle	2	r = √2 = 1.41421+	1.414213572	−9.78e-09	-0.000	reproduced
Dominoes in a circle	3	r = √13/2 = 1.80277+	1.802775664	−2.59e-08	-0.000	reproduced
Dominoes in a circle	4	r = 1.97949+	1.979495622	−5.62e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026
Dominoes in a circle	5	r = 2.18039+	2.180565951	−1.76e-04	-0.008	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	6	r = √5 = 2.23606+	2.355851580	−1.20e-01	-5.357	behind
Dominoes in a circle	7	r = 2.51459+	2.553320800	−3.87e-02	-1.540	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	8	r = 2.65851+	2.771078977	−1.13e-01	-4.234	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	9	r = 2.76860+	2.790411610	−2.18e-02	-0.788	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	10	r = 2.93560+	2.968324834	−3.27e-02	-1.115	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a circle	11	r = 3.08701+	3.261265267	−1.74e-01	-5.645	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a circle	12	r = √10 = 3.16227+	3.354102051	−1.92e-01	-6.066	behind	Found by Maurizio Morandi in May 2026.
Dominoes in a circle	13	r = 3.27852+	3.411424409	−1.33e-01	-4.054	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	14	r = 3.37689+	4.123106481	−7.46e-01	-22.098	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	15	r = 3.48515+	4.031304647	−5.46e-01	-15.671	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	16	r = √13 = 3.60555+	4.189231151	−5.84e-01	-16.188	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	17	r = √53/2 = 3.64005+	5.024947378	−1.3849	-38.046	behind	Found by Maurizio Morandi in May 2026.
Dominoes in a circle	18	r = 3.78121+	6.097649283	−2.3164	-61.262	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	19	r = 3.85867+	4.718350745	−8.60e-01	-22.279	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a circle	20	r = 3.99407+	6.105805323	−2.1117	-52.872	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	21	r = 4.09448+	5.958624644	−1.8641	-45.528	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a circle	22	r = 4.17546+	5.075849911	−9.00e-01	-21.564	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a circle	23	r = 4.25369+	5.089167530	−8.35e-01	-19.641	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a circle	24	r = 4.27200+	4.957647158	−6.86e-01	-16.050	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a circle	25	r = 4.40723+	4.938754903	−5.32e-01	-12.060	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a domino	2	s = (2+√2)/√3 = 1.971+	1.971197126	−6.34e-09	-0.000	reproduced	Found by Erich Friedman in April 2026.
Dominoes in a domino	3	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Dominoes in a domino	4	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Dominoes in a domino	5	s = 5/2 = 2.5	2.500000038	−3.77e-08	-0.000	reproduced
Dominoes in a domino	6	s = 2.916+	3.000000060	−8.40e-02	-2.881	behind	Found by Erich Friedman in April 2026.
Dominoes in a domino	7	s = 3	3.000000051	−5.09e-08	-0.000	reproduced
Dominoes in a domino	8	s = 3	3.000000058	−5.83e-08	-0.000	reproduced
Dominoes in a domino	9	s = 3	3.000000056	−5.58e-08	-0.000	reproduced
Dominoes in a domino	10	s = 7/2 = 3.5	3.664214321	−1.64e-01	-4.692	behind
Dominoes in a domino	11	s = (5+√41)/3 = 3.801+	4.000000084	−1.99e-01	-5.234	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a domino	12	s = 5/2+√2 = 3.914+	4.000000080	−8.58e-02	-2.192	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a domino	13	s = 4	4.000000717	−7.17e-07	-0.000	reproduced	Inherited published construction at n=14; not a newly discovered record
Dominoes in a domino	14	s = 4	4.000000075	−7.55e-08	-0.000	reproduced
Dominoes in a domino	15	s = 4	4.000000076	−7.64e-08	-0.000	reproduced
Dominoes in a domino	16	s = 4	4.000000076	−7.56e-08	-0.000	reproduced
Dominoes in a domino	17	s = 9/2 = 4.5	5.001023009	−5.01e-01	-11.134	behind
Dominoes in a domino	18	s = 9/2 = 4.5	5.000989215	−5.01e-01	-11.133	behind
Dominoes in a domino	19	s = 3(5+√2)/4 = 4.81066+	5.562846023	−7.52e-01	-15.636	behind	Found by Maurizio Morandi in June 2026.
Dominoes in a domino	20	s = 4.95714+	5.001331199	−4.42e-02	-0.891	behind	Found by Maurizio Morandi in June 2026.
Dominoes in a domino	21	s = 5	5.000041971	−4.20e-05	-0.001	behind
Dominoes in a domino	22	s = 5	5.000338294	−3.38e-04	-0.007	behind
Dominoes in a domino	23	s = 5	5.008172231	−8.17e-03	-0.163	behind
Dominoes in a domino	24	s = 5	5.002673455	−2.67e-03	-0.053	behind
Dominoes in a domino	25	s = 5	5.422196621	−4.22e-01	-8.444	behind
Dominoes in a hexagon	2	s = 2/3^(1/4) = 1.51967+	1.519671390	−1.83e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	3	s = √2(3)^(1/4) = 1.86120+	1.861209754	−3.62e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	4	s = 1+2/√3 = 2.15470+	2.154700584	−4.58e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	5	s = 4/√3 = 2.30940+	2.309401130	−5.35e-08	-0.000	reproduced
Dominoes in a hexagon	6	s = 1+5√3/6 = 2.44337+	2.484192223	−4.08e-02	-1.671	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	7	s = 2.63126+	2.728312749	−9.71e-02	-3.688	behind	Found by Aapo Lipponen in July 2026.
Dominoes in a hexagon	8	s = 2.85220+	2.925149827	−7.29e-02	-2.558	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	9	s = 2.93631+	3.008565343	−7.23e-02	-2.461	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	10	s = 3.20593+	3.256415977	−5.05e-02	-1.575	behind	Found by Aapo Lipponen in July 2026.
Dominoes in a hexagon	11	s = 3.33391+	3.464101684	−1.30e-01	-3.905	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	12	s = 3.44304+	3.712075123	−2.69e-01	-7.814	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	13	s = 3.52702+	3.783747508	−2.57e-01	-7.279	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	14	s = 3.65080+	3.729744582	−7.89e-02	-2.162	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	15	s = 2(12)^(1/4) = 3.72241+	3.839768568	−1.17e-01	-3.153	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a hexagon	16	s = 3.87030+	4.136727688	−2.66e-01	-6.884	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	17	s = 4.00242+	5.288683986	−1.2863	-32.137	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	18	s = 2+7√3/6 = 4.02072+	5.289629599	−1.2689	-31.559	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a hexagon	19	s = 4.19677+	5.289624885	−1.0929	-26.040	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a hexagon	20	s = 4.35104+	5.296773352	−9.46e-01	-21.736	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	21	s = 4.43949+	5.351392485	−9.12e-01	-20.541	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	22	s = 4.54229+	7.618976811	−3.0767	-67.734	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	23	s = 2+3√3/2 = 4.59807+	7.618976811	−3.0209	-65.699	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a hexagon	24	s = 2+3√3/2 = 4.59807+	8.234304398	−3.6362	-79.082	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a hexagon	25	s = 3+√3 = 4.73205+	5.561505550	−8.29e-01	-17.528	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a hexagon	26	s = 4+√3/2 = 4.86602+	5.472264976	−6.06e-01	-12.459	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a hexagon	27	s = 4.95289+	5.747765321	−7.95e-01	-16.049	behind	Found by Jonathan Viquerat in September 2026.
Dominoes in a hexagon	28	s = 5.07598+	5.973286992	−8.97e-01	-17.678	behind	Found by Luke Kaiser in September 2026.
Dominoes in a hexagon	29	s = 2+11√3/6 = 5.17542+	5.985148835	−8.10e-01	-15.646	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a hexagon	30	s = 2+11√3/6 = 5.17542+	5.915773090	−7.40e-01	-14.305	behind	Found by Maurizio Morandi in July 2026.
Dominoes in a pentagon	2	s = 1.86166+	1.861668580	−8.58e-06	-0.000	reproduced	Found by Aapo Lipponen in July 2026.
Dominoes in a pentagon	3	s = 2.31933+	2.319335621	−5.62e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	4	s = 2.58859+	2.588595825	−5.83e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	5	s = 2.80725+	2.807256341	−6.34e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	6	s = 2.98883+	2.988831868	−1.87e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	7	s = 3.24589+	3.348544123	−1.03e-01	-3.163	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	8	s = 3.49269+	3.625397753	−1.33e-01	-3.800	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	9	s = 3.65963+	3.724506406	−6.49e-02	-1.773	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	10	s = 3.82264+	4.099176614	−2.77e-01	-7.234	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	11	s = 3.94761+	4.235426774	−2.88e-01	-7.291	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	12	s = 4.13414+	4.583006550	−4.49e-01	-10.858	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	13	s = 4.26767+	4.517430129	−2.50e-01	-5.852	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	14	s = 4.50050+	4.590747710	−9.02e-02	-2.005	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a pentagon	15	s = 4.59464+	4.998455594	−4.04e-01	-8.789	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	16	s = 4.73238+	5.177480406	−4.45e-01	-9.405	behind	Found by Luke Kaiser in September 2026.
Dominoes in a pentagon	17	s = 4.84579+	6.734573009	−1.8888	-38.978	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	18	s = 4+√((5+√5)/8) = 4.95105+	5.705831203	−7.55e-01	-15.245	behind	Found by Maurizio Morandi in August 2026.
Dominoes in a pentagon	19	s = 5.16530+	6.736905931	−1.5716	-30.426	behind	Found by Luke Kaiser in September 2026.
Dominoes in a pentagon	20	s = 5.26425+	6.735815416	−1.4716	-27.954	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	21	s = 5.40180+	8.125643305	−2.7238	-50.425	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	22	s = 5.53463+	7.841464892	−2.3068	-41.680	behind	Found by Luke Kaiser in September 2026.
Dominoes in a pentagon	23	s = 5.63467+	8.341418491	−2.7067	-48.037	behind	Found by Luke Kaiser in September 2026.
Dominoes in a pentagon	24	s = 5.70796+	8.216228778	−2.5083	-43.943	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	25	s = 5.84981+	9.810023859	−3.9602	-67.698	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	26	s = 5.94561+	6.877327575	−9.32e-01	-15.671	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	27	s = 6.03477+	7.061050962	−1.0263	-17.006	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	28	s = 6.19946+	6.948189078	−7.49e-01	-12.077	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	29	s = 6.27249+	7.365628172	−1.0931	-17.427	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a pentagon	30	s = 6.36194+	6.969608465	−6.08e-01	-9.552	behind	Found by Jonathan Viquerat in August 2026.
Dominoes in a square	2	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Dominoes in a square	4	s = 3	3.000000001	−1.20e-09	-0.000	reproduced
Dominoes in a square	6	s = 4	4.000000071	−7.14e-08	-0.000	reproduced
Dominoes in a square	7	s = 4	4.000000020	−1.98e-08	-0.000	reproduced
Dominoes in a square	8	s = 4	4.000000076	−7.56e-08	-0.000	reproduced
Dominoes in a square	9	s = 4.86784+	4.949747573	−8.19e-02	-1.683	behind	Found by Aapo Lipponen in July 2026.
Dominoes in a square	10	s = 5	5.121320461	−1.21e-01	-2.426	behind
Dominoes in a square	11	s = 5	5.414213672	−4.14e-01	-8.284	behind
Dominoes in a square	12	s = 5	6.000116312	−1.0001	-20.002	behind
Dominoes in a square	13	s = 5+1/√2 = 5.70710+	6.000000124	−2.93e-01	-5.132	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a square	14	s = 3+2√2 = 5.82842+	6.414226503	−5.86e-01	-10.051	behind	Found by Maurizio Morandi in June 2026.
Dominoes in a square	15	s = 6	6.822875799	−8.23e-01	-13.715	behind
Dominoes in a square	16	s = 6	6.935562758	−9.36e-01	-15.593	behind
Dominoes in a square	17	s = 6	7.778312345	−1.7783	-29.639	behind
Dominoes in a square	18	s = 6	7.648133372	−1.6481	-27.469	behind
Dominoes in a square	19	s = 47/7 = 6.71428+	7.721835226	−1.0075	-15.006	behind	Found by Maurizio Morandi in June 2026.
Dominoes in a square	20	s = 11/2+√2 = 6.91421+	8.013618476	−1.0994	-15.901	behind	Found by Maurizio Morandi in August 2026.
Dominoes in a square	21	s = 7	9.086373717	−2.0864	-29.805	behind
Dominoes in a square	22	s = 7	13.826037772	−6.8260	-97.515	behind
Dominoes in a square	23	s = 7	13.826037772	−6.8260	-97.515	behind
Dominoes in a square	24	s = 7	13.826037772	−6.8260	-97.515	behind
Dominoes in a square	25	s = 7+1/√2 = 7.70710+	9.034663827	−1.3276	-17.225	behind	Found by Maurizio Morandi in August 2026.
Dominoes in a square	26	s = 5+2√2 = 7.82842+	9.042364424	−1.2139	-15.507	behind	Found by Maurizio Morandi in August 2026.
Dominoes in a square	27	s = 8	9.024764774	−1.0248	-12.810	behind
Dominoes in a square	28	s = 8	10.007672727	−2.0077	-25.096	behind
Dominoes in a square	29	s = 8	9.758040876	−1.7580	-21.976	behind
Dominoes in a square	30	s = 8	10.201265042	−2.2013	-27.516	behind
Dominoes in a square	31	s = 8	10.021216664	−2.0212	-25.265	behind
Dominoes in a square	32	s = 8	11.280449867	−3.2804	-41.006	behind
Dominoes in a tan	2	s = 1+2√2 = 3.82842+	3.828427141	−1.63e-08	-0.000	reproduced
Dominoes in a tan	3	s = 3√2 = 4.24264+	4.242640689	−1.70e-09	-0.000	reproduced
Dominoes in a tan	4	s = 2+2√2 = 4.82842+	4.949747487	−1.21e-01	-2.513	behind	Found by Erich Friedman in May 2026
Dominoes in a tan	5	s = 1+3√2 = 5.24264+	5.242640722	−3.44e-08	-0.000	reproduced	Found by Erich Friedman in May 2026.
Dominoes in a tan	6	s = 4√2 = 5.65685+	5.828427241	−1.72e-01	-3.033	behind
Dominoes in a tan	7	s = 2+3√2 = 6.24264+	6.242640808	−1.21e-07	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Dominoes in a tan	8	s = 5+√2 = 6.41421+	6.949747611	−5.36e-01	-8.349	behind	Found by Erich Friedman in May 2026.
Dominoes in a tan	9	s = 4+2√2 = 6.82842+	7.242772052	−4.14e-01	-6.068	behind	Found by Erich Friedman in May 2026.
Dominoes in a tan	10	s = 5√2 = 7.07106+	7.414213714	−3.43e-01	-4.853	behind
Dominoes in a tan	11	s = 6+√2 = 7.41421+	7.949747633	−5.36e-01	-7.223	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a tan	12	s = 5+2√2 = 7.82842+	8.242640855	−4.14e-01	-5.291	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a tan	13	s = 8	8.967995051	−9.68e-01	-12.100	behind	Found by Erich Friedman in May 2026.
Dominoes in a tan	14	s = 4+3√2 = 8.24264+	9.949747679	−1.7071	-20.711	behind	Found by Maurizio Morandi in May 2026.
Dominoes in a tan	15	s = 6√2 = 8.48528+	10.000000641	−1.5147	-17.851	behind
Dominoes in a tan	16	s = 6+2√2 = 8.82842+	10.001773869	−1.1733	-13.291	behind	Found by Erich Friedman in May 2026.
Dominoes in a tan	17	s = 9	10.174693094	−1.1747	-13.052	behind	Found by Maurizio Morandi in May 2026.
Dominoes in a tan	18	s = 5+3√2 = 9.24264+	10.852483305	−1.6098	-17.418	behind	Found by Maurizio Morandi in May 2026.
Dominoes in a tan	19	s = 1+6√2 = 9.48528+	10.875017059	−1.3897	-14.651	behind	Found by Maurizio Morandi in May 2026.
Dominoes in a tan	20	s = 7+2√2 = 9.82842+	10.945021958	−1.1166	-11.361	behind	Found by Jonathan Viquerat in May 2026.
Dominoes in a triangle	2	s = 2+4/√3 = 4.30940+	4.309401093	−1.65e-08	-0.000	reproduced
Dominoes in a triangle	3	s = 2+4/√3 = 4.30940+	4.309401078	−1.72e-09	-0.000	reproduced
Dominoes in a triangle	4	s = 5.38188+	5.381887117	−7.12e-06	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	5	s = 2+2√3 = 5.46410+	5.464101720	−1.05e-07	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	6	s = 4+4/√3 = 6.30940+	6.593261137	−2.84e-01	-4.499	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	7	s = 6.61394+	6.824295573	−2.10e-01	-3.180	behind	Found by Aapo Lipponen in July 2026.
Dominoes in a triangle	8	s = 6+2/√3 = 7.15470+	7.154700687	−1.49e-07	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	9	s = 5+4/√3 = 7.30940+	7.773502867	−4.64e-01	-6.349	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	10	s = 3+8/√3 = 7.61880+	8.309401230	−6.91e-01	-9.064	behind	Found by Bhavithran Ananthan in July 2026.
Dominoes in a triangle	11	s = 7+2/√3 = 8.15470+	8.774817295	−6.20e-01	-7.604	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	12	s = 6+4/√3 = 8.30940+	9.050844872	−7.41e-01	-8.923	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	13	s = 4+8/√3 = 8.61880+	11.237605022	−2.6188	-30.385	behind	Found by Bhavithran Ananthan in July 2026.
Dominoes in a triangle	14	s = 3+10/√3 = 8.77350+	10.543917130	−1.7704	-20.179	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a triangle	15	s = 7+4/√3 = 9.30940+	11.577881637	−2.2685	-24.368	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	16	s = 6+2√3 = 9.46410+	10.618804158	−1.1547	-12.201	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a triangle	17	s = 4+10/√3 = 9.77350+	20.276851996	−10.5033	-107.468	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	18	s = 3+4√3 = 9.92820+	11.261762920	−1.3336	-13.432	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	19	s = 8+4/√3 = 10.30940+	12.145062618	−1.8357	-17.806	behind	Found by Jonathan Viquerat in April 2026.
Dominoes in a triangle	20	s = 7+2√3 = 10.46410+	20.276851996	−9.8128	-93.775	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a triangle	21	s = 2+5√3 = 10.66025+	20.276851996	−9.6166	-90.210	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a triangle	22	s = 4(1+√3) = 10.92820+	14.684670420	−3.7565	-34.374	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a triangle	23	s = 10+2/√3 = 11.15470+	20.276851996	−9.1222	-81.779	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a triangle	24	s = 9+4/√3 = 11.30940+	13.881024773	−2.5716	-22.739	behind	Found by Maurizio Morandi in April 2026.
Dominoes in a triangle	25	s = 7+8/√3 = 11.61880+	12.545271602	−9.26e-01	-7.974	behind	Found by Maurizio Morandi in June 2026.
Dominoes in a triangle	26	s = 11.79418+	13.315425509	−1.5212	-12.898	behind	Found by Aapo Lipponen in July 2026.
Dominoes in a triangle	27	s = 4+14/√3 = 12.08290+	14.136302978	−2.0534	-16.994	behind	Found by Maurizio Morandi in June 2026.
Dominoes in an L	2	s = 3/2 = 1.5	1.500000013	−1.31e-08	-0.000	reproduced
Dominoes in an L	3	s = (6+√2)/4 = 1.853+	1.853553424	−3.36e-08	-0.000	reproduced	Found by Erich Friedman in April 2026.
Dominoes in an L	4	s = 2	2.000000001	−8.01e-10	-0.000	reproduced
Dominoes in an L	5	s = 2	2.000000004	−3.62e-09	-0.000	reproduced
Dominoes in an L	6	s = 2	2.000000003	−2.69e-09	-0.000	reproduced
Dominoes in an L	7	s = 5/2 = 2.5	3.000000064	−5.00e-01	-20.000	behind
Dominoes in an L	8	s = 5/2 = 2.5	3.000000038	−5.00e-01	-20.000	behind
Dominoes in an L	9	s = 2.87746+	3.000000060	−1.23e-01	-4.259	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an L	10	s = 3	3.500000074	−5.00e-01	-16.667	behind
Dominoes in an L	11	s = 3	3.500000048	−5.00e-01	-16.667	behind
Dominoes in an L	12	s = 3	3.529371966	−5.29e-01	-17.646	behind
Dominoes in an L	13	s = 3	4.000000760	−1.0000	-33.333	behind
Dominoes in an L	14	s = 3+√2/4 = 3.353+	4.000476619	−6.47e-01	-19.294	behind	Found by Maurizio Morandi in April 2026.
Dominoes in an L	15	s = 7/2 = 3.5	4.000008069	−5.00e-01	-14.286	behind
Dominoes in an L	16	s = 7/2 = 3.5	4.000080256	−5.00e-01	-14.288	behind
Dominoes in an L	17	s = (10+9√2)/6 = 3.787+	4.500853092	−7.13e-01	-18.824	behind	Found by Maurizio Morandi in April 2026.
Dominoes in an L	18	s = (11+6√2)/5 = 3.897+	5.087083787	−1.1900	-30.537	behind	Found by Maurizio Morandi in April 2026.
Dominoes in an L	19	s = 4	5.022765148	−1.0228	-25.569	behind
Dominoes in an L	20	s = 4	11.534995484	−7.5350	-188.375	behind
Dominoes in an L	21	s = 4	11.534995484	−7.5350	-188.375	behind
Dominoes in an L	22	s = 4	11.565677377	−7.5657	-189.142	behind
Dominoes in an L	23	s = 4	11.586131972	−7.5861	-189.653	behind
Dominoes in an L	24	s = 4	11.586131972	−7.5861	-189.653	behind
Dominoes in an octagon	2	s = √(4–2√2) = 1.08239+	1.082392210	−9.97e-09	-0.000	reproduced
Dominoes in an octagon	3	s = √(5–√2–√(8√2–9)) = 1.43690+	1.436905902	−2.33e-08	-0.000	reproduced	Found by Maurizio Morandi in May 2026.
Dominoes in an octagon	4	s = 1.57337+	1.573372066	−2.07e-06	-0.000	reproduced	Found by Maurizio Morandi in May 2026.
Dominoes in an octagon	5	s = 1.71644+	1.720930940	−4.49e-03	-0.262	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	6	s = √(6–√2–√(20√2–26)) = 1.75339+	1.908943103	−1.56e-01	-8.871	behind	Found by Maurizio Morandi in May 2026.
Dominoes in an octagon	7	s = 2.00516+	2.071067853	−6.59e-02	-3.287	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	8	s = 5(√2–1) = 2.07106+	2.071067868	−5.59e-08	-0.000	reproduced
Dominoes in an octagon	9	s = 2.19803+	2.287462702	−8.94e-02	-4.069	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	10	s = 2.32394+	2.627886550	−3.04e-01	-13.079	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	11	s = 2.44911+	2.490798972	−4.17e-02	-1.702	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	12	s = 6(√2–1) = 2.48528+	2.528319423	−4.30e-02	-1.732	behind
Dominoes in an octagon	13	s = 2.56556+	2.705658795	−1.40e-01	-5.461	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	14	s = 2.67740+	2.866210760	−1.89e-01	-7.052	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	15	s = 2.80446+	2.913022614	−1.09e-01	-3.871	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	16	s = 2√(5–√2–√(8√2–9)) = 2.87381+	3.214231714	−3.40e-01	-11.846	behind	Found by Maurizio Morandi in June 2026.
Dominoes in an octagon	17	s = 2.92223+	3.986025325	−1.0638	-36.404	behind	Found by Aapo Lipponen in July 2026.
Dominoes in an octagon	18	s = 9–17√2/4 = 2.98959+	3.986109639	−9.97e-01	-33.333	behind	Found by Maurizio Morandi in August 2026.
Dominoes in an octagon	19	s = 3.08791+	3.986114683	−8.98e-01	-29.088	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	20	s = 3.16881+	3.985452694	−8.17e-01	-25.771	behind	Found by Jonathan Viquerat in June 2026.
Dominoes in an octagon	21	s = 8(√2–1) = 3.31370+	3.987360542	−6.74e-01	-20.329	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	22	s = 8(√2–1) = 3.31370+	4.021885550	−7.08e-01	-21.371	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	23	s = (26–9√2)/4 = 3.31801+	5.400296006	−2.0823	-62.757	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	24	s = 4(13–5√2)/7 = 3.38796+	3.944860950	−5.57e-01	-16.438	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	25	s = 2√(6–√2–√(20√2–26)) = 3.50679+	4.076121878	−5.69e-01	-16.235	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	26	s = 2√(6–√2–√(20√2–26)) = 3.50679+	4.938024007	−1.4312	-40.813	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	27	s = 10–9/√2 = 3.63603+	4.067096036	−4.31e-01	-11.855	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	28	s = 9(√2–1) = 3.72792+	4.409651433	−6.82e-01	-18.287	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	29	s = 22(3–2√2) = 3.77460+	4.359295979	−5.85e-01	-15.490	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	30	s = (42–19√2)/4 = 3.78248+	4.331693795	−5.49e-01	-14.520	behind	Found by Maurizio Morandi in July 2026.
Dominoes in an octagon	31	s = 3.80663+	4.612620504	−8.06e-01	-21.173	behind	Found by Aapo Lipponen in July 2026.
Hexagons in a circle	2	r = √13/2 = 1.802+	1.802775649	−1.10e-08	-0.000	reproduced
Hexagons in a circle	3	r = 2	2.000000032	−3.17e-08	-0.000	reproduced
Hexagons in a circle	4	r = (21–√145)/4 = 2.239+	2.239601380	−2.47e-08	-0.000	reproduced	Found by Maurizio Morandi in March 2026.
Hexagons in a circle	5	r = 2.471+	2.645751338	−1.75e-01	-7.072	behind	Found by Maurizio Morandi in March 2026.
Hexagons in a circle	6	r = √7 = 2.645+	2.645751339	−2.84e-08	-0.000	reproduced
Hexagons in a circle	7	r = √7 = 2.645+	2.645751349	−3.83e-08	-0.000	reproduced
Hexagons in a circle	8	r = 2.984+	2.984724774	−7.25e-04	-0.024	reproduced	Found by Maurizio Morandi in March 2026.
Hexagons in a circle	9	r = 3.301+	3.305379380	−4.38e-03	-0.133	behind	Found by Maurizio Morandi in March 2026.
Hexagons in a circle	10	r = 3.48172+	3.488984368	−7.26e-03	-0.209	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	11	r = 3.59003+	3.597900881	−7.87e-03	-0.219	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	12	r = √13 = 3.605+	3.762040847	−1.56e-01	-4.341	behind	Found by Maurizio Morandi in March 2026.
Hexagons in a circle	13	r = 3.82289+	3.860633255	−3.77e-02	-0.987	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	14	r = 3.87755+	3.885382759	−7.83e-03	-0.202	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	15	r = 4.08154+	4.121615713	−4.01e-02	-0.982	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	16	r = 4.13960+	4.444390744	−3.05e-01	-7.363	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	17	r = 4.30158+	4.373837784	−7.23e-02	-1.680	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	18	r = √19 = 4.35889+	4.527922805	−1.69e-01	-3.878	behind
Hexagons in a circle	19	r = √19 = 4.35889+	4.644759676	−2.86e-01	-6.558	behind
Hexagons in a circle	20	r = 4.62527+	4.865563117	−2.40e-01	-5.195	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	21	r = 4.68305+	5.009438441	−3.26e-01	-6.970	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	22	r = 4.89204+	5.010566045	−1.19e-01	-2.423	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	23	r = 4.98608+	5.199571083	−2.13e-01	-4.282	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	24	r = 5.08387+	5.369717297	−2.86e-01	-5.623	behind	Found by Jake Loyd in June 2026.
Hexagons in a circle	25	r = 5.18804+	5.669270315	−4.81e-01	-9.276	behind	Found by Haowei Lin in June 2026.
Hexagons in a circle	26	r = 5.25746+	6.025732252	−7.68e-01	-14.613	behind	Found by Haowei Lin in June 2026.
Hexagons in a circle	27	r = 5.28167+	6.055914281	−7.74e-01	-14.659	behind	Found by Haowei Lin in June 2026.
Hexagons in a domino	2	s = 1.8946+	1.894691519	−9.15e-05	-0.005	reproduced	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	3	s = 6–2√3 = 2.53589+	2.535898400	−1.55e-08	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	4	s = 22–11√3 = 2.94744+	2.947441134	−1.75e-08	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	5	s = 7(2√3–3) = 3.24871+	3.248710331	+9.75e-07	0.000	beaten	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	6	s = 21(15–2√3)/71 = 3.41202+	3.419365245	−7.34e-03	-0.215	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	7	s = 3.48722+	3.494206555	−6.99e-03	-0.200	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a domino	8	s = 3.6906+	3.690675039	−7.50e-05	-0.002	reproduced	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	9	s = (36+5√3)/11 = 4.06002+	4.060023165	−7.09e-08	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	10	s = 9(2√3–3) = 4.17691+	4.536641585	−3.60e-01	-8.612	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	11	s = 4.5036+	4.564022250	−6.04e-02	-1.342	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	12	s = 41(18–5√3)/83 = 4.6136+	5.196152519	−5.83e-01	-12.627	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	13	s = 4.8137+	6.928203331	−2.1145	-43.927	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	14	s = 25(6–√3)/22 = 4.84994+	5.000309499	−1.50e-01	-3.100	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	15	s = 56(27–4√3)/227 = 4.95163+	6.928216897	−1.9766	-39.918	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	16	s = 3√3 = 5.19615+	6.928217088	−1.7321	-33.334	behind
Hexagons in a domino	17	s = 3√3 = 5.19615+	5.752256384	−5.56e-01	-10.702	behind
Hexagons in a domino	18	s = 31(4–√3)/13 = 5.40818+	5.975844280	−5.68e-01	-10.496	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	19	s = 5.65222+	8.665647531	−3.0134	-53.314	behind	Found by Jonathan Viquerat in September 2026.
Hexagons in a domino	20	s = 5.8012+	8.683954142	−2.8828	-49.692	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a domino	21	s = 5.85640+	8.691507330	−2.8351	-48.410	behind	Found by Thomas Greenleaf in June 2026.
Hexagons in a domino	22	s = 6.06943+	8.774494654	−2.7051	-44.569	behind	Found by Jonathan Viquerat in September 2026.
Hexagons in a domino	23	s = 6.25797+	8.767611834	−2.5096	-40.103	behind	Found by Jonathan Viquerat in September 2026.
Hexagons in a hexagon	2	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Hexagons in a hexagon	3	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Hexagons in a hexagon	4	s = 7/3 = 2.333+	2.333333334	−9.33e-10	-0.000	reproduced
Hexagons in a hexagon	5	s = 8/3 = 2.666+	2.666666677	−1.05e-08	-0.000	reproduced	Found by Erich Friedman in March 2015.
Hexagons in a hexagon	6	s = 5/√3 = 2.886+	2.896311913	−9.56e-03	-0.331	behind	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	7	s = 5/√3 = 2.886+	2.886753673	−2.33e-06	-0.000	reproduced	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	8	s = (51+5√3)/18 = 3.314+	3.314458618	−6.03e-08	-0.000	reproduced	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	9	s = (24+5√3)/9 = 3.628+	3.628917182	−6.66e-08	-0.000	reproduced	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	10	s = 2 + √3 = 3.732+	3.732051689	−8.81e-07	-0.000	reproduced	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	11	s = 2+10/3√3 = 3.92450+	3.947381159	−2.29e-02	-0.583	behind	Found by Johann Schellhorn in July 2025.
Hexagons in a hexagon	12	s = 3.94164+	4.000000082	−5.84e-02	-1.481	behind	Found by Alpha Evolve in May 2025.
Hexagons in a hexagon	13	s = 4	4.265561155	−2.66e-01	-6.639	behind
Hexagons in a hexagon	14	s = 4.26899+	4.290872320	−2.19e-02	-0.513	behind	Found by Dominik Kamp in April 2026.
Hexagons in a hexagon	15	s = 4.44727+	4.532105344	−8.48e-02	-1.908	behind	Found by Alex Kravatsky et al in February 2026.
Hexagons in a hexagon	16	s = 4.52746+	4.871243150	−3.44e-01	-7.593	behind	Found by Alex Kravatsky et al in February 2026.
Hexagons in a hexagon	17	s = 4.6136+	4.780362995	−1.67e-01	-3.615	behind	Found by Alex Kravatsky et al in February 2026.
Hexagons in a hexagon	18	s = 8/√3 = 4.618+	4.938694440	−3.20e-01	-6.927	behind	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	19	s = 8/√3 = 4.618+	4.850465189	−2.32e-01	-5.017	behind	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	20	s = 5	5.171116207	−1.71e-01	-3.422	behind
Hexagons in a hexagon	21	s = 5	5.536024435	−5.36e-01	-10.720	behind
Hexagons in a hexagon	22	s = (39+8√3)/10 = 5.285+	5.569511398	−2.84e-01	-5.371	behind	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	23	s = 5.39998+	5.783203944	−3.83e-01	-7.097	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in a hexagon	24	s = 19√3/6 = 5.484+	5.978937525	−4.94e-01	-9.010	behind	Found by Maurizio Morandi in April 2015.
Hexagons in a hexagon	25	s = 5.62390+	6.181009254	−5.57e-01	-9.906	behind	Found by Alex Kravatsky et al in February 2026.
Hexagons in a hexagon	26	s = 5.70972+	6.175666681	−4.66e-01	-8.161	behind	Found by Alex Kravatsky et al in February 2026.
Hexagons in a hexagon	27	s = 5.71415+	6.426122798	−7.12e-01	-12.460	behind	Found by Alex Kravatsky et al in February 2026.
Hexagons in a hexagon	28	s = 5.90893+	6.397927320	−4.89e-01	-8.276	behind	Found by Alex Kravatsky et al in February 2026.
Hexagons in a hexagon	29	s = 6	6.432971352	−4.33e-01	-7.216	behind
Hexagons in a hexagon	30	s = 6	7.062221605	−1.0622	-17.704	behind
Hexagons in a hexagon	31	s = 6	6.706315216	−7.06e-01	-11.772	behind
Hexagons in a hexagon	32	s = 6.26088+	7.102541074	−8.42e-01	-13.443	behind	Found by Aristotle Papowitz in July 2026.
Hexagons in a hexagon	33	s = 6.26580+	6.658727688	−3.93e-01	-6.271	behind	Found by Jonathan Viquerat in September 2026.
Hexagons in a pentagon	2	s = 2.46585+	2.465852284	−2.28e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	3	s = 2.74282+	2.742825935	−5.93e-06	-0.000	reproduced	Found by Ethan Riddle in May 2026.
Hexagons in a pentagon	4	s = 3.01521+	3.015218981	−8.98e-06	-0.000	reproduced	Found by Bhavithran Ananthan in July 2026.
Hexagons in a pentagon	5	s = 3.21972+	3.219728524	−8.52e-06	-0.000	reproduced	Found by Aristotle Papowitz in July 2026.
Hexagons in a pentagon	6	s = 3.54952+	3.549533503	−1.35e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	7	s = 3.79749+	3.797494365	−4.37e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	8	s = 4.14916+	4.149170844	−1.08e-05	-0.000	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a pentagon	9	s = 4.34314+	4.343145221	−5.22e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	10	s = 4.55810+	4.578964486	−2.09e-02	-0.458	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	11	s = 4.71959+	4.778956981	−5.94e-02	-1.258	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a pentagon	12	s = 4.91850+	4.961093839	−4.26e-02	-0.866	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	13	s = 5.10107+	5.149011524	−4.79e-02	-0.940	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a pentagon	14	s = 5.29198+	5.325191516	−3.32e-02	-0.628	behind	Found by Jake Loyd in June 2026.
Hexagons in a pentagon	15	s = 5.41337+	5.600818781	−1.87e-01	-3.463	behind	Found by Jake Loyd in June 2026.
Hexagons in a pentagon	16	s = 5.61409+	5.934800671	−3.21e-01	-5.713	behind	Found by Jake Loyd in June 2026.
Hexagons in a pentagon	17	s = 5.82103+	5.884664059	−6.36e-02	-1.093	behind	Found by Jake Loyd in June 2026.
Hexagons in a pentagon	18	s = 5.94471+	6.074711333	−1.30e-01	-2.187	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	19	s = 6.10977+	6.242229813	−1.32e-01	-2.168	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a pentagon	20	s = 6.24667+	7.708143704	−1.4615	-23.396	behind	Found by Jake Loyd in June 2026.
Hexagons in a pentagon	21	s = 6.39216+	6.714489879	−3.22e-01	-5.043	behind	Found by Jonathan Viquerat in August 2026.
Hexagons in a pentagon	22	s = 6.53472+	6.869893045	−3.35e-01	-5.129	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a pentagon	23	s = 6.66271+	7.151149158	−4.88e-01	-7.331	behind	Found by Jake Loyd in June 2026.
Hexagons in a pentagon	24	s = 6.77466+	8.370210804	−1.5956	-23.552	behind	Found by Jake Loyd in June 2026.
Hexagons in a pentagon	25	s = 6.89098+	8.001724212	−1.1107	-16.119	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a pentagon	26	s = 7.04734+	8.495333442	−1.4480	-20.547	behind	Found by Aristotle Papowitz in July 2026.
Hexagons in a pentagon	27	s = 7.15307+	9.046289354	−1.8932	-26.467	behind	Found by Aristotle Papowitz in July 2026.
Hexagons in a pentagon	28	s = 7.24805+	8.515888289	−1.2678	-17.492	behind	Found by Jonathan Viquerat in August 2026.
Hexagons in a pentagon	29	s = 7.37833+	8.415060921	−1.0367	-14.051	behind	Found by Jonathan Viquerat in August 2026.
Hexagons in a pentagon	30	s = 7.45985+	8.792875613	−1.3330	-17.869	behind	Found by Aristotle Papowitz in July 2026.
Hexagons in a pentagon	31	s = 7.63254+	8.644352966	−1.0118	-13.257	behind	Found by Jonathan Viquerat in August 2026.
Hexagons in a pentagon	32	s = 7.76619+	8.753834638	−9.88e-01	-12.717	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a square	2	s = (1+2√3)/√2 = 3.156+	3.156596572	−4.79e-08	-0.000	reproduced
Hexagons in a square	3	s = 9(6–√3)/11 = 3.491+	3.491958453	−2.30e-08	-0.000	reproduced	Found by Maurizio Morandi in March 2026.
Hexagons in a square	4	s = (7–√3)/√2 = 3.725+	3.725002621	−2.43e-08	-0.000	reproduced	Found by Maurizio Morandi in March 2026.
Hexagons in a square	5	s = 7(3–√3)/2 = 4.437+	4.437822251	−7.79e-08	-0.000	reproduced	Found by Maurizio Morandi in March 2026.
Hexagons in a square	6	s = 20(9–2√3)/23 = 4.813+	4.823801872	−9.98e-03	-0.207	behind	Found by Maurizio Morandi in March 2026.
Hexagons in a square	7	s = 3√3 = 5.196+	5.196152441	−1.85e-08	-0.000	reproduced
Hexagons in a square	8	s = 3√3 = 5.196+	5.359067220	−1.63e-01	-3.135	behind
Hexagons in a square	9	s = (13–3√3)/√2 = 5.518+	5.586322333	−6.82e-02	-1.235	behind	Found by Maurizio Morandi in March 2026.
Hexagons in a square	10	s = 6.10469+	6.139442905	−3.48e-02	-0.569	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a square	11	s = 6.33218+	6.342786233	−1.06e-02	-0.167	behind	Found by Maksymilian Jankowski in April 2026.
Hexagons in a square	12	s = 43(5–√3)/22 = 6.387+	6.463461426	−7.61e-02	-1.192	behind	Found by Maurizio Morandi in March 2026.
Hexagons in a square	13	s = 6.75549+	6.880645342	−1.25e-01	-1.853	behind	Found by Timo Berthold et al in May 2026.
Hexagons in a square	14	s = 4√3 = 6.928+	6.956779049	−2.86e-02	-0.412	behind
Hexagons in a square	15	s = 6.96367+	7.471144551	−5.07e-01	-7.287	behind	Found by Maksymilian Jankowski in April 2026.
Hexagons in a square	16	s = (19–5√3)/√2 = 7.311+	7.415858192	−1.05e-01	-1.430	behind	Found by Maurizio Morandi in April 2026.
Hexagons in a square	17	s = 7.60383+	7.778788062	−1.75e-01	-2.301	behind	Found by Maksymilian Jankowski in April 2026.
Hexagons in a square	18	s = 32(9–2√3)/23 = 7.702+	8.057253714	−3.55e-01	-4.611	behind	Found by Maurizio Morandi in April 2026.
Hexagons in a square	19	s = 25(3–√3)/4 = 7.924+	8.299552265	−3.75e-01	-4.731	behind	Found by Maurizio Morandi in April 2026.
Hexagons in a square	20	s = 74(21–4√3)/131 = 7.948+	8.460022282	−5.11e-01	-6.430	behind	Found by Maurizio Morandi in April 2026.
Hexagons in a square	21	s = 8.381+	8.665052996	−2.84e-01	-3.389	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a square	22	s = 8.568+	9.018322083	−4.50e-01	-5.256	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a square	23	s = 5√3 = 8.660+	13.724525455	−5.0643	-58.479	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a square	24	s = 8.795+	13.724525455	−4.9295	-56.049	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a square	25	s = 30(4√3–3)/13 = 9.065+	10.992588105	−1.9275	-21.263	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a square	26	s = 9.22083+	9.957930689	−7.37e-01	-7.994	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a square	27	s = 9.27733+	10.267225640	−9.90e-01	-10.670	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a tan	2	s = 4.46410+	4.464101631	−1.63e-06	-0.000	reproduced
Hexagons in a tan	3	s = 4.94974+	4.949747470	−7.47e-06	-0.000	reproduced
Hexagons in a tan	4	s = 5.75097+	5.750978159	−8.16e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	5	s = 6.50265+	6.502661852	−1.19e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	6	s = 6.74289+	6.742898534	−8.53e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	7	s = 7.39923+	7.451570129	−5.23e-02	-0.707	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	8	s = 7.83340+	7.844935132	−1.15e-02	-0.147	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	9	s = 8.28267+	8.300494200	−1.78e-02	-0.215	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	10	s = 8.53604+	8.956949535	−4.21e-01	-4.931	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	11	s = 9.06093+	9.083100057	−2.22e-02	-0.245	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	12	s = 9.41319+	9.808078324	−3.95e-01	-4.195	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	13	s = 9.70087+	10.085138449	−3.84e-01	-3.961	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a tan	14	s = 10.03836+	11.044219291	−1.0059	-10.020	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	15	s = 10.32919+	10.731380570	−4.02e-01	-3.894	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	16	s = 10.71312+	11.345669627	−6.33e-01	-5.904	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a tan	17	s = 10.97884+	11.714795042	−7.36e-01	-6.703	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	18	s = 11.27299+	11.868267179	−5.95e-01	-5.281	behind	Found by Jonathan Viqueratl in May 2026.
Hexagons in a tan	19	s = 11.49013+	12.148766810	−6.59e-01	-5.732	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a tan	20	s = 11.77041+	13.275079044	−1.5047	-12.783	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a triangle	2	s = 5	5.000000011	−1.15e-08	-0.000	reproduced
Hexagons in a triangle	3	s = 5	5.000000002	−2.00e-09	-0.000	reproduced
Hexagons in a triangle	4	s = 6	6.000000005	−4.96e-09	-0.000	reproduced
Hexagons in a triangle	5	s = 5(1+√3)/2 = 6.8301+	6.830127141	−1.22e-07	-0.000	reproduced	Found by Maurizio Morandi in April 2015.
Hexagons in a triangle	6	s = 2(1+√6) = 6.89897+	6.898982802	−3.32e-06	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Hexagons in a triangle	7	s = 8	8.000000137	−1.37e-07	-0.000	reproduced
Hexagons in a triangle	8	s = 25/3 = 8.3333+	8.865835592	−5.33e-01	-6.390	behind	Found by Erich Friedman in April 2015.
Hexagons in a triangle	9	s = 8.64494+	8.675138082	−3.02e-02	-0.349	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a triangle	10	s = 5√3 = 8.6602+	8.764598459	−1.04e-01	-1.205	behind
Hexagons in a triangle	11	s = 9.54823+	9.732051452	−1.84e-01	-1.925	behind	Found by Jonathan Viquerat in April 2026.
Hexagons in a triangle	12	s = 9.96429+	10.196152877	−2.32e-01	-2.327	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a triangle	13	s = 10.28857+	10.392305051	−1.04e-01	-1.008	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in a triangle	14	s = 6√3 = 10.3923+	10.488697833	−9.64e-02	-0.928	behind
Hexagons in a triangle	15	s = 6√3 = 10.3923+	10.464654431	−7.23e-02	-0.696	behind
Hexagons in a triangle	16	s = 11.36383+	12.196174505	−8.32e-01	-7.325	behind	Found by Timo Berthold et al in May 2026.
Hexagons in a triangle	17	s = 11.63454+	12.572461275	−9.38e-01	-8.062	behind	Found by Jonathan Viquerat in August 2026.
Hexagons in a triangle	18	s = 11.91421+	13.029916592	−1.1157	-9.365	behind	Found by Jake Loyd in May 2026.
Hexagons in a triangle	19	s = 12	19.667778098	−7.6678	-63.898	behind
Hexagons in a triangle	20	s = 7√3 = 12.1243+	19.667778098	−7.5434	-62.217	behind
Hexagons in a triangle	21	s = 7√3 = 12.1243+	19.667778098	−7.5434	-62.217	behind
Hexagons in a triangle	22	s = 12.99518+	19.667778098	−6.6726	-51.347	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in a triangle	23	s = 13.39989+	19.667778098	−6.2679	-46.776	behind	Found by Jake Loyd in June 2026.
Hexagons in a triangle	24	s = 13.61925+	24.475470406	−10.8562	-79.712	behind	Found by Thomas Greenleaf in June 2026.
Hexagons in a triangle	25	s = 13.77683+	15.786986112	−2.0102	-14.591	behind	Found by Jake Loyd in June 2026.
Hexagons in a triangle	26	s = 7√3 = 13.85677+	14.897119261	−1.0403	-7.508	behind
Hexagons in a triangle	27	s = 7√3 = 13.85677+	15.968049392	−2.1113	-15.236	behind
Hexagons in a triangle	28	s = 7√3 = 13.85677+	16.117254390	−2.2605	-16.313	behind
Hexagons in a triangle	29	s = 14.78557+	17.334885045	−2.5493	-17.242	behind	Found by Haowei Lin in July 2026.
Hexagons in a triangle	30	s = 15	16.575405853	−1.5754	-10.503	behind
Hexagons in a triangle	31	s = 15	16.189924820	−1.1899	-7.933	behind
Hexagons in a triangle	32	s = 15.47573+	17.978142432	−2.5024	-16.170	behind	Found by Haowei Lin in July 2026.
Hexagons in an L	2	s = √3 = 1.73205+	1.732050808	−6.93e-10	-0.000	reproduced
Hexagons in an L	3	s = 1.88648+	1.886483830	−3.83e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	4	s = 2.41072+	2.418007196	−7.29e-03	-0.302	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	5	s = 2.59807+	2.598076247	−6.25e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	6	s = 2.90072+	2.900723594	−3.59e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	7	s = 3.08493+	3.443626629	−3.59e-01	-11.627	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	8	s = 3.26559+	3.464101664	−1.99e-01	-6.079	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	9	s = 3.39536+	3.405656499	−1.03e-02	-0.303	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	10	s = 2√3 = 3.46410+	3.512423236	−4.83e-02	-1.395	behind
Hexagons in an L	11	s = 3.48851+	3.609361560	−1.21e-01	-3.464	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	12	s = 3.68106+	3.684491867	−3.43e-03	-0.093	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	13	s = 3.94486+	8.387491960	−4.4426	-112.618	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	14	s = 4.09579+	4.257605903	−1.62e-01	-3.951	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	15	s = 4.2134+	4.302904307	−8.95e-02	-2.124	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	16	s = 4.27526+	4.401413787	−1.26e-01	-2.951	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	17	s = 4.51508+	10.384615385	−5.8695	-129.998	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	18	s = 4.59397+	5.078013810	−4.84e-01	-10.537	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	19	s = 4.70835+	5.205848545	−4.97e-01	-10.566	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	20	s = 4.75480+	10.384615385	−5.6298	-118.403	behind	Found by Jonathan Viquerat in June 2026.
Hexagons in an L	21	s = 4.90214+	10.384615385	−5.4825	-111.838	behind	Found by Jonathan Viquerat in September 2026.
Hexagons in an L	22	s = 4.93211+	10.384615385	−5.4525	-110.551	behind	Found by Jonathan Viquerat in September 2026.
Hexagons in an octagon	2	s = 2√3/(1+√2) = 1.43487+	1.434877871	−5.74e-10	-0.000	reproduced
Hexagons in an octagon	3	s = 3+2√6–2√2–2√3 = 1.60645+	1.606450746	−6.43e-10	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	4	s = 1.75630+	1.756300707	−7.07e-07	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	5	s = 1.98707+	1.987076725	−6.72e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	6	s = 2.16435+	2.166020224	−1.67e-03	-0.077	behind	Found by Nicolas Campailla in May 2026.
Hexagons in an octagon	7	s = 2.18284+	2.185668273	−2.83e-03	-0.130	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	8	s = 2.40792+	2.407922002	−2.00e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	9	s = 2.62665+	2.636445709	−9.80e-03	-0.373	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	10	s = 2.74238+	2.742384153	−4.15e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	11	s = 4√3/(1+√2) = 2.86975+	2.885242304	−1.55e-02	-0.540	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	12	s = 2.92139+	3.027680626	−1.06e-01	-3.638	behind	Found by Timo Berthold et al in May 2026.
Hexagons in an octagon	13	s = 3.07201+	3.143116464	−7.11e-02	-2.315	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	14	s = 3.13475+	3.157819696	−2.31e-02	-0.736	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	15	s = 3.28379+	3.362235696	−7.84e-02	-2.389	behind	Found by Timo Berthold et al in May 2026.
Hexagons in an octagon	16	s = 3.37007+	3.571869948	−2.02e-01	-5.988	behind	Found by Timo Berthold et al in May 2026.
Hexagons in an octagon	17	s = 3.47655+	3.516474770	−3.99e-02	-1.148	behind	Found by Jake Loyd in June 2026.
Hexagons in an octagon	18	s = 3.56008+	3.683443095	−1.23e-01	-3.465	behind	Found by Timo Berthold et al in May 2026.
Hexagons in an octagon	19	s = 5√3/(1+√2) = 3.58719+	4.538707595	−9.52e-01	-26.525	behind	Found by Jonathan Viquerat in May 2026.
Hexagons in an octagon	20	s = 3.72605+	4.016764710	−2.91e-01	-7.802	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in an octagon	21	s = 3.81006+	4.136951741	−3.27e-01	-8.580	behind	Found by Bhavithran Ananthan in July 2026.
Hexagons in an octagon	22	s = 3.91915+	4.164957823	−2.46e-01	-6.272	behind	Found by Thomas Greenleaf in June 2026.
L's in a circle	2	r = √13/2 = 1.802+	1.838477657	−3.57e-02	-1.981	behind	Found by David W. Cantrell in June 2005.
L's in a circle	3	r = √305/8 = 2.183+	2.183031178	−2.88e-08	-0.000	reproduced	Found by Maurizio Morandi in August 2007.
L's in a circle	4	r = √5 = 2.236+	2.467669237	−2.32e-01	-10.358	behind	Found by Erich Friedman in June 2005.
L's in a circle	5	r = 2.56858+	2.763481354	−1.95e-01	-7.588	behind	Found by Jake Loyd in June 2026.
L's in a circle	6	r = √8249/32 = 2.838+	3.061121007	−2.23e-01	-7.853	behind	Found by Erich Friedman in June 2005.
L's in a circle	7	r = √34/2 = 2.915+	3.208854588	−2.93e-01	-10.064	behind	Found by Erich Friedman in June 2005.
L's in a circle	8	r = √10 = 3.162+	3.384913517	−2.23e-01	-7.041	behind	Found by Erich Friedman in June 2005.
L's in a circle	9	r = 3.36482+	3.610428337	−2.46e-01	-7.299	behind	Found by Jake Loyd in June 2026.
L's in a circle	10	r = 3.490+	3.928315044	−4.38e-01	-12.559	behind	Found by Maurizio Morandi in June 2026.
L's in a circle	11	r = 3.68165+	3.919051677	−2.37e-01	-6.448	behind	Found by Jake Loyd in June 2026.
L's in a circle	12	r = 3.80266+	4.107245442	−3.05e-01	-8.010	behind	Found by Jake Loyd in June 2026.
L's in a circle	13	r = 3.94961+	4.318399154	−3.69e-01	-9.337	behind	Found by Jake Loyd in June 2026.
L's in a circle	14	r = √17 = 4.123+	4.492495939	−3.69e-01	-8.959	behind	Found by David W. Cantrell in August 2007.
L's in a circle	15	r = 4.214+	4.563783701	−3.50e-01	-8.301	behind	Found by Maurizio Morandi in August 2007.
L's in a circle	16	r = √74/2 = 4.301+	4.754124388	−4.53e-01	-10.532	behind	Found by Maurizio Morandi in September 2008.
L's in a circle	17	r = 2√5 = 4.472+	7.260349632	−2.7882	-62.348	behind	Found by Maurizio Morandi in September 2008.
L's in a circle	18	r = √86609/64 = 4.598+	5.732257668	−1.1339	-24.661	behind	Found by Maurizio Morandi in September 2008.
L's in a circle	19	r = 4.70546+	5.883265836	−1.1778	-25.031	behind	Found by Jake Loyd in June 2026.
L's in a circle	20	r = 4.77260+	6.923008768	−2.1504	-45.057	behind	Found by Jake Loyd in June 2026.
L's in a circle	21	r = 5.09246+	6.525857119	−1.4334	-28.147	behind	Found by Jonathan Viquerat in August 2026.
L's in a circle	22	r = 5.21859+	7.663230497	−2.4446	-46.845	behind	Found by Jonathan Viquerat in August 2026.
L's in a circle	23	r = 5.30468+	9.364387102	−4.0597	-76.531	behind	Found by Jonathan Viquerat in August 2026.
L's in a domino	2	s = 2	2.000000011	−1.07e-08	-0.000	reproduced
L's in a domino	3	s = 5/2 = 2.5	2.500000001	−1.00e-09	-0.000	reproduced
L's in a domino	4	s = 6(1+√2)/5 = 2.897+	3.000000013	−1.03e-01	-3.553	behind	Found by Erich Friedman in April 2026.
L's in a domino	5	s = 3	3.444816898	−4.45e-01	-14.827	behind
L's in a domino	6	s = 3	3.483539543	−4.84e-01	-16.118	behind
L's in a domino	7	s = 7/3+√2 = 3.747+	4.341649352	−5.94e-01	-15.855	behind	Found by Erich Friedman in April 2026.
L's in a domino	8	s = 4	4.536992906	−5.37e-01	-13.425	behind
L's in a domino	9	s = 4	5.000000108	−1.0000	-25.000	behind
L's in a domino	10	s = 4	5.000000100	−1.0000	-25.000	behind
L's in a domino	11	s = 3(6+√2)/5 = 4.448+	6.000000118	−1.5515	-34.880	behind	Found by Maurizio Morandi in April 2026.
L's in a domino	12	s = 9/2 = 4.5	8.000000172	−3.5000	-77.778	behind
L's in a domino	13	s = (14+11√2)/6 = 4.926+	8.002559537	−3.0765	-62.454	behind	Found by Maurizio Morandi in April 2026.
L's in a domino	14	s = 5	8.000159989	−3.0002	-60.003	behind
L's in a domino	15	s = 5	8.000016005	−3.0000	-60.000	behind
L's in a domino	16	s = 5	8.000001608	−3.0000	-60.000	behind
L's in a domino	17	s = 3+7√2/4 = 5.474+	9.212404601	−3.7375	-68.278	behind	Found by Maurizio Morandi in April 2026.
L's in a domino	18	s = 11/2 = 5.5	13.017465126	−7.5175	-136.681	behind
L's in a domino	19	s = 3+2√2 = 5.828+	13.146567148	−7.3181	-125.569	behind	Found by Maurizio Morandi in April 2026.
L's in a domino	20	s = 6	10.269617076	−4.2696	-71.160	behind
L's in a domino	21	s = 6	13.237697987	−7.2377	-120.628	behind
L's in a domino	22	s = 6	13.305461945	−7.3055	-121.758	behind
L's in a domino	23	s = 6	11.841299391	−5.8413	-97.355	behind
L's in a domino	24	s = 6	8.046248128	−2.0462	-34.104	behind
L's in a hexagon	2	s = 12^(1/4) = 1.861+	1.861209730	−1.22e-08	-0.000	reproduced	Found by Maurizio Morandi in May 2026.
L's in a hexagon	3	s = 1/2 + √3 = 2.232+	2.345396256	−1.13e-01	-5.078	behind	Found by Maurizio Morandi in May 2026.
L's in a hexagon	4	s = 2.50337+	2.597045137	−9.37e-02	-3.742	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	5	s = 2.85988+	3.016462860	−1.57e-01	-5.475	behind	Found by Jake Loyd in May 2026
L's in a hexagon	6	s = 3.04254+	3.318885630	−2.76e-01	-9.083	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	7	s = 3.25359+	3.539669664	−2.86e-01	-8.793	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	8	s = 2√3 = 3.464+	3.762930226	−2.99e-01	-8.627	behind
L's in a hexagon	9	s = 3.65374+	3.930940507	−2.77e-01	-7.587	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	10	s = 3.80531+	4.143900492	−3.39e-01	-8.898	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	11	s = 7/√3 = 4.041+	4.461048203	−4.20e-01	-10.383	behind
L's in a hexagon	12	s = 4.15868+	4.618802245	−4.60e-01	-11.064	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	13	s = 4.33273+	4.803621321	−4.71e-01	-10.868	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	14	s = 4.46716+	4.813593917	−3.46e-01	-7.755	behind	Found by Jake Loyd in June 2026.
L's in a hexagon	15	s = 8/√3 = 4.61880+	5.120332514	−5.02e-01	-10.858	behind
L's in a hexagon	16	s = 4.72806+	5.433634557	−7.06e-01	-14.923	behind	Found by Aapo Lipponen in July 2026.
L's in a hexagon	17	s = 4.93064+	6.035739735	−1.1051	-22.413	behind	Found by Aaden Abraham in July 2026.
L's in a hexagon	18	s = 5.09795+	6.673249933	−1.5753	-30.901	behind	Found by Aapo Lipponen in July 2026.
L's in a hexagon	19	s = 3√3 = 5.19615+	7.040614373	−1.8445	-35.497	behind	Found by Maurizio Morandi in July 2026.
L's in a hexagon	20	s = 2+17√3/9 = 5.27165+	7.118434938	−1.8468	-35.032	behind	Found by Maurizio Morandi in August 2026.
L's in a hexagon	21	s = (13+5√3)/4 = 5.41506+	7.558329719	−2.1433	-39.580	behind	Found by Maurizio Morandi in July 2026.
L's in a hexagon	22	s = 7(1+1/√3)/2 = 5.52072+	8.759410839	−3.2387	-58.664	behind	Found by Maurizio Morandi in August 2026.
L's in a hexagon	23	s = 7√6/3 = 5.71547+	10.143986460	−4.4285	-77.483	behind	Found by Aaden Abraham in July 2026.
L's in a hexagon	24	s = 10/√3 = 5.77350+	7.077975211	−1.3045	-22.594	behind	Found by Aaden Abraham in July 2026.
L's in a hexagon	25	s = 7/3+2√3 = 5.79743+	9.643089934	−3.8457	-66.334	behind	Found by Maurizio Morandi in August 2026.
L's in a hexagon	26	s = 9/2+5√3/6 = 5.94337+	7.630189065	−1.6868	-28.381	behind	Found by Maurizio Morandi in August 2026.
L's in a hexagon	27	s = 9/2+11√3/12 = 6.08771+	7.869582818	−1.7819	-29.270	behind	Found by Maurizio Morandi in July 2026.
L's in a hexagon	28	s = 7/2+19√/12 = 6.24241+	7.618922824	−1.3765	-22.051	behind	Found by Maurizio Morandi in July 2026.
L's in a hexagon	29	s = 11/√3 = 6.35085+	7.589993756	−1.2391	-19.511	behind	Found by Aaden Abraham in July 2026.
L's in a hexagon	30	s = (11+√3)/2 = 6.36602+	7.909114481	−1.5431	-24.239	behind	Found by Maurizio Morandi in July 2026.
L's in a pentagon	2	s = 2.33322+	2.333225281	−5.28e-06	-0.000	reproduced
L's in a pentagon	3	s = 2.79081+	2.835425599	−4.46e-02	-1.599	behind	Found by Jonathan Viquerat in May 2026.
L's in a pentagon	4	s = 3.07149+	3.071493579	−3.58e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
L's in a pentagon	5	s = 3.41569+	3.628915130	−2.13e-01	-6.243	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	6	s = 3.74743+	4.134462790	−3.87e-01	-10.328	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	7	s = 3.96756+	4.230121801	−2.63e-01	-6.618	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	8	s = 4.25642+	4.517958503	−2.62e-01	-6.145	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	9	s = 4.50713+	4.786312832	−2.79e-01	-6.194	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	10	s = 3√5–3+3√(1–2/√5) = 4.65767+	4.902938987	−2.20e-01	-4.723	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	11	s = 4.86103+	5.538785772	−6.78e-01	-13.943	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	12	s = 5.07519+	5.778475179	−7.03e-01	-13.857	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	13	s = 5.29475+	5.812022740	−5.17e-01	-9.770	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	14	s = 5.49989+	6.095204608	−5.95e-01	-10.824	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	15	s = 5.63035+	6.060767991	−4.30e-01	-7.645	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	16	s = 5.77738+	6.680502684	−9.03e-01	-15.632	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	17	s = 5.92697+	10.492009055	−4.5650	-77.021	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	18	s = 6.16318+	11.020255647	−4.8571	-78.808	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	19	s = 6.33939+	11.020255647	−4.6809	-73.838	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	20	s = 6.45886+	10.220767605	−3.7619	-58.244	behind	Found by Jake Loyd in June 2026.
L's in a pentagon	21	s = 4√5–7/2+√(25–10√5) = 7.06887+	9.364280804	−2.2954	-32.472	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	22	s = 4√5–7/2+√(25–10√5) = 7.06887+	10.004285589	−2.9354	-41.526	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	23	s = 4√5–7/2+√(25–10√5) = 7.06887+	11.069242081	−4.0004	-56.591	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	24	s = 4√5–7/2+√(25–10√5) = 7.06887+	11.609522917	−4.5407	-64.234	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	25	s = 7√5–14+18√(1–2/√5) = 7.50103+	11.920508152	−4.4195	-58.918	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	26	s = 7√5–14+18√(1–2/√5) = 7.50103+	9.303046965	−1.8020	-24.024	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	27	s = 7√5–14+18√(1–2/√5) = 7.50103+	9.972582730	−2.4716	-32.950	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	28	s = 4√5–3+6√(1–2/√5) = 7.89379+	10.322476598	−2.4287	-30.767	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	29	s = 4√5–3+6√(1–2/√5) = 7.89379+	9.521708583	−1.6279	-20.623	behind	Found by Maurizio Morandi in August 2026.
L's in a pentagon	30	s = 4√5–3+6√(1–2/√5) = 7.89379+	11.165285070	−3.2715	-41.444	behind	Found by Maurizio Morandi in August 2026.
L's in a square	2	s = 3	3.000000017	−1.66e-08	-0.000	reproduced
L's in a square	3	s = (3 + 3√2) / 2 = 3.621+	3.621320345	−1.45e-09	-0.000	reproduced	Found by Serhiy Grabarchuk in July 2005.
L's in a square	4	s = 4	4.000000002	−1.60e-09	-0.000	reproduced
L's in a square	5	s = 4	4.687741129	−6.88e-01	-17.194	behind
L's in a square	6	s = 7 / √2 = 4.949+	5.275317162	−3.26e-01	-6.578	behind	Found by Erich Friedman in June 2005.
L's in a square	7	s = 5	5.656854363	−6.57e-01	-13.137	behind
L's in a square	8	s = 5	6.000000120	−1.0000	-20.000	behind
L's in a square	9	s = 5.81902+	6.645035139	−8.26e-01	-14.195	behind	Found by Aapo Lipponen in July 2026.
L's in a square	10	s = 6	7.132382144	−1.1324	-18.873	behind
L's in a square	11	s = 6	7.299831795	−1.2998	-21.664	behind
L's in a square	12	s = 6	7.313362386	−1.3134	-21.889	behind
L's in a square	13	s = 4 + 2√2 = 6.828+	7.473593583	−6.45e-01	-9.449	behind	Found by Maurizio Morandi in June 2012.
L's in a square	14	s = 7	7.952471846	−9.52e-01	-13.607	behind
L's in a square	15	s = 7	8.416180304	−1.4162	-20.231	behind
L's in a square	16	s = 7	8.244400143	−1.2444	-17.777	behind
L's in a square	17	s = 19/3 + √2 = 7.747+	14.057367653	−6.3098	-81.449	behind	Found by Maurizio Morandi in June 2012.
L's in a square	18	s = 13/2 + √2 = 7.914+	14.358103120	−6.4439	-81.424	behind	Found by Maurizio Morandi in June 2012.
L's in a square	19	s = 8	14.542274428	−6.5423	-81.778	behind
L's in a square	20	s = 8	14.666649860	−6.6666	-83.333	behind
L's in a square	21	s = 8	14.666649860	−6.6666	-83.333	behind
L's in a square	22	s = 3 + 4√2 = 8.656+	14.309939963	−5.6531	-65.308	behind	Found by Maurizio Morandi in June 2012.
L's in a square	23	s = 15/2 + √2 = 8.914+	14.713535043	−5.7993	-65.059	behind	Found by Maurizio Morandi in June 2012.
L's in a square	24	s = 9	14.713535043	−5.7135	-63.484	behind
L's in a square	25	s = 9	16.946097911	−7.9461	-88.290	behind
L's in a square	26	s = 9	16.995300062	−7.9953	-88.837	behind
L's in a square	27	s = 9	12.660226443	−3.6602	-40.669	behind
L's in a square	28	s = 7 + 2√2 = 9.828+	13.664413142	−3.8360	-39.031	behind	Found by Maurizio Morandi in May 2026.
L's in a tan	2	s = 3√2 = 4.242+	4.242640703	−1.54e-08	-0.000	reproduced
L's in a tan	3	s = 5	5.000000002	−2.00e-09	-0.000	reproduced
L's in a tan	4	s = 4√2 = 5.656+	5.828427144	−1.72e-01	-3.033	behind	Found by Maurizio Morandi in July 2012
L's in a tan	5	s = 2 + 3√2 = 6.242+	7.000000140	−7.57e-01	-12.133	behind	Found by Maurizio Morandi in July 2012.
L's in a tan	6	s = 7	7.518603915	−5.19e-01	-7.409	behind
L's in a tan	7	s = 7	8.089702162	−1.0897	-15.567	behind
L's in a tan	8	s = 11/√2 = 7.778+	8.242640852	−4.64e-01	-5.972	behind
L's in a tan	9	s = 8	9.828427340	−1.8284	-22.855	behind
L's in a tan	10	s = 6√2 = 8.485+	9.639221000	−1.1539	-13.600	behind
L's in a tan	11	s = 9	9.806865381	−8.07e-01	-8.965	behind
L's in a tan	12	s = 9	10.519765275	−1.5198	-16.886	behind
L's in a tan	13	s = 2 + 11/√2 = 9.778+	10.801843699	−1.0237	-10.469	behind	Found by Maurizio Morandi in July 2012.
L's in a tan	14	s = 7√2 = 9.899+	11.242640896	−1.3431	-13.569	behind
L's in a tan	15	s = 10	12.000000240	−2.0000	-20.000	behind
L's in a tan	16	s = 15/√2 = 10.606+	12.000248175	−1.3936	-13.140	behind
L's in a tan	17	s = 8 + 2√2 = 10.828+	27.074383955	−16.2460	-150.037	behind	Found by Maurizio Morandi in January 2025.
L's in a tan	18	s = 11	27.074383955	−16.0744	-146.131	behind
L's in a tan	19	s = 8√2 = 11.313+	27.074383955	−15.7607	-139.315	behind	Found by Maurizio Morandi in January 2025.
L's in a tan	20	s = 4 + 11/√2 = 11.778+	27.074383955	−15.2962	-129.871	behind	Found by Maurizio Morandi in January 2025.
L's in a tan	21	s = 12	27.074383955	−15.0744	-125.620	behind
L's in a tan	22	s = 12	20.350826640	−8.3508	-69.590	behind
L's in a triangle	2	s = 4 + 2/√3 = 5.15470+	5.154700555	−1.69e-08	-0.000	reproduced
L's in a triangle	3	s = 3 + 3√3/2 = 5.59807+	5.598076230	−1.83e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
L's in a triangle	4	s = 6.58646+	6.618802177	−3.23e-02	-0.491	behind	Found by Jonathan Viquerat in May 2026.
L's in a triangle	5	s = 6 + 2/√3 = 7.15470+	7.386751560	−2.32e-01	-3.243	behind	Found by Jonathan Viquerat in May 2026.
L's in a triangle	6	s = 4 + 2√3 = 7.46410+	7.732050966	−2.68e-01	-3.590	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	7	s = 7 + 2/√3 = 8.15470+	8.386751521	−2.32e-01	-2.846	behind	Found by Jonathan Viquerat in May 2026.
L's in a triangle	8	s = 7 + √3 = 8.73205+	9.308578255	−5.77e-01	-6.602	behind	Found by Jonathan Viquerat in May 2026.
L's in a triangle	9	s = 5 + 7/√3 = 9.04145+	9.732100329	−6.91e-01	-7.639	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	10	s = 6 + 2√3 = 9.46410+	10.865758811	−1.4017	-14.810	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	11	s = 4 + 10/√3 = 9.77350+	10.543669567	−7.70e-01	-7.880	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	12	s = 10.30175+	11.370444926	−1.0687	-10.374	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	13	s = 9 + √3 = 10.73205+	12.158158321	−1.4261	-13.288	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	14	s = 7 + 7/√3 = 11.04145+	12.231856569	−1.1904	-10.781	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	15	s = 5 + 11/√3 = 11.35085+	12.567448649	−1.2166	-10.718	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	16	s = 10 + √3 = 11.73205+	12.964135636	−1.2321	-10.502	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	17	s = 4 + 14/√3 = 12.08290+	22.310726063	−10.2278	-84.647	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	18	s = 9 + 2√3 = 12.46410+	16.578293007	−4.1142	-33.008	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	19	s = 11 + √3 = 12.73205+	23.268902038	−10.5369	-82.758	behind	Found by Maurizio Morandi in May 2026.
L's in a triangle	20	s = 13.00966+	23.268902038	−10.2592	-78.859	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	21	s = 13.30935+	23.275880592	−9.9665	-74.884	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	22	s = 2 + 20/√3 = 13.54700+	21.357452222	−7.8104	-57.654	behind	Found by Maurizio Morandi in June 2026.
L's in a triangle	23	s = 14.19776+	23.402541191	−9.2048	-64.833	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	24	s = 15.00964+	31.623429943	−16.6138	-110.687	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	25	s = 15.20151+	16.680390457	−1.4789	-9.729	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	26	s = 15.22482+	17.772760850	−2.5479	-16.735	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	27	s = 15.65894+	18.165805275	−2.5069	-16.009	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	28	s = 16.14341+	18.452075130	−2.3087	-14.301	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	29	s = 16.39862+	18.362939918	−1.9643	-11.979	behind	Found by Aapo Lipponen in July 2026.
L's in a triangle	30	s = 16.46648+	18.862173703	−2.3957	-14.549	behind	Found by Aapo Lipponen in July 2026.
L's in an L	2	s = 2	2.000000017	−1.69e-08	-0.000	reproduced
L's in an L	3	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
L's in an L	4	s = 2	2.500000035	−5.00e-01	-25.000	behind
L's in an L	5	s = 5/2 = 2.5	3.000000046	−5.00e-01	-20.000	behind
L's in an L	6	s = 1 + 4√2/3 = 2.885+	3.048528197	−1.63e-01	-5.647	behind	Found by Maurizio Morandi in July 2012.
L's in an L	7	s = 3	3.000000008	−7.80e-09	-0.000	reproduced
L's in an L	8	s = 3	3.839276416	−8.39e-01	-27.976	behind
L's in an L	9	s = 3	7.710864295	−4.7109	-157.029	behind
L's in an L	10	s = 7/2 = 3.5	3.988150985	−4.88e-01	-13.947	behind
L's in an L	11	s = 7/3 + √2 = 3.747+	4.156933769	−4.09e-01	-10.926	behind	Found by Maurizio Morandi in July 2012.
L's in an L	12	s = (19 + 9√2) / 8 = 3.965+	4.110446064	−1.44e-01	-3.643	behind	Found by Maurizio Morandi in July 2012.
L's in an L	13	s = 4	4.400680653	−4.01e-01	-10.017	behind
L's in an L	14	s = 4	6.000000124	−2.0000	-50.000	behind
L's in an L	15	s = 4	5.000000112	−1.0000	-25.000	behind
L's in an L	16	s = 4	10.690929953	−6.6909	-167.273	behind
L's in an L	17	s = 9/2 = 4.5	14.268289244	−9.7683	-217.073	behind
L's in an L	18	s = 9/2 = 4.5	14.268289244	−9.7683	-217.073	behind
L's in an L	19	s = 3 + 5√2/4 = 4.767+	14.310149817	−9.5424	-200.176	behind	Found by Maurizio Morandi in June 2026.
L's in an L	20	s = 3(6 + 5√2)/8 = 4.901+	12.684202747	−7.7826	-158.795	behind	Found by Maurizio Morandi in June 2026.
L's in an L	21	s = 5	14.310149817	−9.3101	-186.203	behind
L's in an L	22	s = 5	13.595394657	−8.5954	-171.908	behind
L's in an L	23	s = 5	13.804875369	−8.8049	-176.098	behind
L's in an L	24	s = 5	6.590604481	−1.5906	-31.812	behind
L's in an L	25	s = 5	6.494794914	−1.4948	-29.896	behind
L's in an octagon	2	s = √(5–√2–√(8√2–9)) = 1.43690+	1.436905880	−5.75e-10	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
L's in an octagon	3	s = 10(3–2√2) = 1.71572+	1.734478077	−1.87e-02	-1.093	behind	Found by Aapo Lipponen in July 2026.
L's in an octagon	4	s = 3(2–√2) = 1.75735+	1.984773653	−2.27e-01	-12.941	behind	Found by Aapo Lipponen in July 2026
L's in an octagon	5	s = 5/(1+√2) = 2.07106+	2.071067850	−3.82e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026
L's in an octagon	6	s = 13(3–2√2) = 2.23044+	2.414213611	−1.84e-01	-8.239	behind	Found by Jonathan Viquerat in May 2026.
L's in an octagon	7	s = 4(2–√2) = 2.34314+	2.574118591	−2.31e-01	-9.857	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	8	s = 6(√2–1) = 2.48528+	2.736661048	−2.51e-01	-10.115	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	9	s = 11(3√2–4) = 2.66904+	2.861793014	−1.93e-01	-7.222	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	10	s = 2(11–√2)/7 = 2.73879+	3.168569617	−4.30e-01	-15.692	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	11	s = 7(√2–1) = 2.89949+	3.139674411	−2.40e-01	-8.284	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	12	s = 5(2–√2) = 2.92893+	3.299621611	−3.71e-01	-12.656	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	13	s = 13(3√2–4) = 3.15432+	3.395292327	−2.41e-01	-7.639	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	14	s = 5(4√2–5) = 3.28427+	3.629072789	−3.45e-01	-10.499	behind	Found by Maurizio Morandi in August 2026.
L's in an octagon	15	s = 25(8–5√2)/7 = 3.31761+	3.686387895	−3.69e-01	-11.116	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	16	s = 20(3–2√2) = 3.43145+	3.915580644	−4.84e-01	-14.108	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	17	s = 6(2–√2) = 3.51471+	5.431974148	−1.9173	-54.549	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	18	s = 25(2–√2)/4 = 3.66116+	4.902827261	−1.2417	-33.914	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	19	s = 9(√2–1) = 3.72792+	5.343371244	−1.6154	-43.334	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	20	s = 22(3–2√2) = 3.77460+	5.451673118	−1.6771	-44.430	behind	Found by Maurizio Morandi in May 2026.
L's in an octagon	21	s = 16(3√2–4) = 3.88225+	5.627420709	−1.7452	-44.953	behind	Found by Maurizio Morandi in August 2026.
L's in an octagon	22	s = 27(2–√2)/4 = 3.95405+	6.257947065	−2.3039	-58.267	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	23	s = 7(2–√2) = 4.10050+	6.489713860	−2.3892	-58.266	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	24	s = 10(√2–1) = 4.14213+	6.761024677	−2.6189	-63.226	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	25	s = 10(√2–1) = 4.14213+	5.275949713	−1.1338	-27.373	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	26	s = 25(3–2√2) = 4.28932+	5.312582517	−1.0233	-23.856	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	27	s = 15(1–1/√2) = 4.39339+	5.407293017	−1.0139	-23.078	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	28	s = 31(2–√2)/4 = 4.53984+	5.575746496	−1.0359	-22.818	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	29	s = 11(√2–1) = 4.55634+	5.435855248	−8.80e-01	-19.303	behind	Found by Maurizio Morandi in July 2026.
L's in an octagon	30	s = 11(√2–1) = 4.55634+	6.365711815	−1.8094	-39.711	behind	Found by Maurizio Morandi in July 2026.
Octagons in a circle	2	r = √(13/4+2√2) = 2.46544+	2.465446649	−1.14e-08	-0.000	reproduced
Octagons in a circle	3	r = 2.71611+	2.716111075	−1.07e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	4	r = √(9/2+3√2) = 2.95679+	2.956795711	−3.19e-08	-0.000	reproduced
Octagons in a circle	5	r = 3.37974+	3.655675235	−2.76e-01	-8.164	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	6	r = 3.69797+	3.697970689	−6.89e-07	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	7	r = 3.77329+	3.773295999	−6.00e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	8	r = 4.12460+	4.124607953	−7.95e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	9	r = 4.46088+	4.460885628	−5.63e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	10	r = 4.72215+	4.734565569	−1.24e-02	-0.263	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	11	r = 4.88201+	4.929121243	−4.71e-02	-0.965	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	12	r = 5.00001+	5.146543931	−1.47e-01	-2.931	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	13	r = 5.23457+	5.266923581	−3.24e-02	-0.618	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	14	r = 5.34130+	5.345142476	−3.84e-03	-0.072	behind	Found by Haowei Lin in July 2026.
Octagons in a circle	15	r = 5.60687+	5.691134773	−8.43e-02	-1.503	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	16	r = 5.73295+	6.073284997	−3.40e-01	-5.936	behind	Found by Haowei Lin in July 2026.
Octagons in a circle	17	r = 5.94448+	6.064521152	−1.20e-01	-2.019	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	18	r = 6.05966+	6.118350517	−5.87e-02	-0.969	behind	Found by Haowei Lin in July 2026.
Octagons in a circle	19	r = 6.07328+	6.358578860	−2.85e-01	-4.698	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a circle	20	r = 6.36724+	6.713383614	−3.46e-01	-5.436	behind	Found by Haowei Lin in July 2026.
Octagons in a circle	21	r = 6.48101+	6.690649984	−2.10e-01	-3.235	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a circle	22	r = 6.70466+	6.857995620	−1.53e-01	-2.287	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a circle	23	r = 6.85820+	8.988126782	−2.1299	-31.057	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a circle	24	r = 6.96998+	7.296705835	−3.27e-01	-4.688	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a circle	25	r = 7.12165+	7.394244302	−2.73e-01	-3.828	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a domino	2	s = 1 + √2 = 2.41421+	2.414213570	−7.42e-09	-0.000	reproduced
Octagons in a domino	3	s = 3.51366+	3.513669803	−9.80e-06	-0.000	reproduced	Found by Aapo Lipponen in July 2026.
Octagons in a domino	4	s = 2 + 7√2/5 = 3.97989+	3.979898989	−1.59e-09	-0.000	reproduced	Found by Aapo Lipponen in July 2026.
Octagons in a domino	5	s = 13/6 + 3/√2 = 4.28798+	4.287987012	−1.72e-09	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	6	s = (16 + 11√2)/7 = 4.50804+	4.508049960	−7.59e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	7	s = 2 + 2√2 = 4.82842+	4.828427207	−8.20e-08	-0.000	reproduced
Octagons in a domino	8	s = 2 + 2√2 = 4.82842+	4.828427127	−2.05e-09	-0.000	reproduced
Octagons in a domino	9	s = 8/3 + 2√2 = 5.49509+	5.700498284	−2.05e-01	-3.738	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	10	s = 3 + 2√2 = 5.82842+	5.889404678	−6.10e-02	-1.046	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	11	s = 16/5 + 2√2 = 6.02842+	6.207784311	−1.79e-01	-2.975	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	12	s = 6.31126+	6.411537575	−1.00e-01	-1.589	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	13	s = 6.51128+	7.242641666	−7.31e-01	-11.232	behind	Found by Aapo Lipponen in July 2026.
Octagons in a domino	14	s = (21 + 13√2)/6 = 6.56412+	9.657047206	−3.0929	-47.119	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	15	s = (47 + 29√2)/13 = 6.77016+	9.657047383	−2.8869	-42.641	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	16	s = 7.10456+	9.656873059	−2.5523	-35.925	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	17	s = 3 + 3√2 = 7.24264+	7.871569831	−6.29e-01	-8.684	behind
Octagons in a domino	18	s = 3 + 3√2 = 7.24264+	7.966311490	−7.24e-01	-9.992	behind
Octagons in a domino	19	s = 7.77123+	13.318018800	−5.5468	-71.376	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	20	s = 8.03947+	12.079133274	−4.0397	-50.248	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a domino	21	s = 8.21837+	12.094717344	−3.8763	-47.167	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a domino	22	s = 8.34004+	12.129142184	−3.7891	-45.433	behind	Found by Thomas Greenleaf in June 2026.
Octagons in a hexagon	2	s = 2.70289+	2.702888728	+1.27e-06	0.000	reproduced
Octagons in a hexagon	3	s = 2.88958+	2.889628784	−4.88e-05	-0.002	behind	Found by Mohamed Metwalli in June 2026.
Octagons in a hexagon	4	s = 11+8√2–16/√3–4√6 = 3.27814+	3.278145237	−1.64e-08	-0.000	reproduced	Found by Mohamed Metwalli in June 2026.
Octagons in a hexagon	5	s = 3.71848+	3.718485425	−5.42e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	6	s = 3.94730+	3.947306375	−6.38e-06	-0.000	reproduced	Found by Aristotle Papowitz in July 2026.
Octagons in a hexagon	7	s = 3.97716+	3.977162459	−2.46e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	8	s = 4.56653+	4.566540278	−1.03e-05	-0.000	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	9	s = 4.93304+	4.933045515	−5.51e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	10	s = 5.06929+	5.133637347	−6.43e-02	-1.269	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	11	s = 5.34796+	5.377745097	−2.98e-02	-0.557	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a hexagon	12	s = 5.38669+	5.515323517	−1.29e-01	-2.388	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	13	s = 5.75470+	5.822456836	−6.78e-02	-1.177	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	14	s = 5.77752+	5.789778162	−1.23e-02	-0.212	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	15	s = 6.13744+	6.167523062	−3.01e-02	-0.490	behind	Found by Bhavithran Ananthan in June 2026.
Octagons in a hexagon	16	s = 6.21438+	6.775071343	−5.61e-01	-9.022	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	17	s = 6.35725+	6.437289606	−8.00e-02	-1.259	behind	Found by Jonathan Viquerat in June 2026.
Octagons in a hexagon	18	s = 6.42774+	6.467228285	−3.95e-02	-0.614	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a hexagon	19	s = 6.44696+	7.123748333	−6.77e-01	-10.498	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a hexagon	20	s = 6.99419+	7.133800501	−1.40e-01	-1.996	behind	Found by Leo Strijbos in August 2026.
Octagons in a pentagon	2	s = 3.35605+	3.356053089	−3.09e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	3	s = 3.74411+	3.744125629	−1.56e-05	-0.000	behind	Found by Bhavithran Ananthan in May 2026.
Octagons in a pentagon	4	s = 4.10125+	4.101259755	−9.76e-06	-0.000	reproduced	Found by Bhavithran Ananthan in July 2026.
Octagons in a pentagon	5	s = 4.33300+	4.338166880	−5.17e-03	-0.119	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	6	s = 4.77007+	4.770075637	−5.64e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	7	s = = 5.25544+	5.255443053	−3.05e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	8	s = 5.61662+	5.616625037	−5.04e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	9	s = 5.96580+	5.985830124	−2.00e-02	-0.336	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	10	s = 6.28146+	6.281467372	−7.37e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	11	s = 6.46576+	6.515201936	−4.94e-02	-0.765	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	12	s = 6.71763+	6.931114687	−2.13e-01	-3.178	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	13	s = 6.97061+	7.006376152	−3.58e-02	-0.513	behind	Found by Aapo Lipponen in July 2026.
Octagons in a pentagon	14	s = 7.16083+	7.164117448	−3.29e-03	-0.046	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a pentagon	16	s = 7.61505+	7.875310565	−2.60e-01	-3.418	behind	Found by Bhavithran Ananthan in June 2026.
Octagons in a pentagon	17	s = 7.91419+	8.054578516	−1.40e-01	-1.774	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a pentagon	18	s = 8.12567+	8.387487104	−2.62e-01	-3.222	behind	Found by Bhavithran Ananthan in June 2026.
Octagons in a pentagon	19	s = 8.34354+	8.613155536	−2.70e-01	-3.231	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a pentagon	20	s = 8.54202+	9.081174548	−5.39e-01	-6.312	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a pentagon	21	s = 8.74315+	9.372095968	−6.29e-01	-7.194	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a pentagon	22	s = 8.96230+	9.106677844	−1.44e-01	-1.611	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a pentagon	23	s = 9.11759+	9.746813799	−6.29e-01	-6.901	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a pentagon	24	s = 9.27761+	9.730830993	−4.53e-01	-4.885	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a pentagon	25	s = 9.45135+	10.466858316	−1.0155	-10.745	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a square	2	s = 2 + 3√2/2 = 4.12132+	4.121320356	−1.20e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a square	3	s = 2 + 2√2 = 4.82842+	4.828427127	−1.93e-09	-0.000	reproduced
Octagons in a square	4	s = 2 + 2√2 = 4.82842+	4.828427127	−1.93e-09	-0.000	reproduced
Octagons in a square	5	s = 3 + 2√2 = 5.82842+	5.828427127	−2.33e-09	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a square	6	s = (11√2+17)/5 = 6.51126+	6.511269959	−1.22e-07	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a square	7	s = (5√2+7)/2 = 7.03553+	7.035534036	−1.30e-07	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a square	8	s = 3 + 3√2 = 7.24264+	7.242640824	−1.37e-07	-0.000	reproduced
Octagons in a square	9	s = 3 + 3√2 = 7.24264+	7.242640821	−1.34e-07	-0.000	reproduced
Octagons in a square	10	s = 4+3√2 = 8.24264+	8.414001666	−1.71e-01	-2.079	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	11	s = 8.57596+	8.748780034	−1.73e-01	-2.015	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	12	s = (23√2+38)/8 = 8.81586+	8.949926470	−1.34e-01	-1.521	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	13	s = 9.19909+	9.596194233	−3.97e-01	-4.317	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	14	s = (7√2+9)/2 = 9.44974+	9.949747665	−5.00e-01	-5.291	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	15	s = 4 + 4√2 = 9.65685+	9.657390707	−5.36e-04	-0.006	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	16	s = 4 + 4√2 = 9.65685+	10.656872570	−1.0000	-10.356	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	17	s = 10.44973+	10.658936943	−2.09e-01	-2.002	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	18	s = (17√2+29)/5 = 10.60832+	11.074818217	−4.66e-01	-4.397	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	19	s = 10.96620+	11.150601088	−1.84e-01	-1.682	behind	Found by Haowei Lin in July 2026.
Octagons in a square	20	s = (39√2+67)/11 = 11.10493+	11.541971331	−4.37e-01	-3.935	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a square	21	s = 11.47891+	18.226728752	−6.7478	-58.784	behind	Found by Grigory Merzon in August 2026.
Octagons in a square	22	s = 11.63403+	18.226728752	−6.5927	-56.667	behind	Found by Grigory Merzon in August 2026.
Octagons in a tan	2	s = 3+2√2 = 5.82842+	5.828427139	−1.41e-08	-0.000	reproduced
Octagons in a tan	3	s = 3+5/√2 = 6.53553+	6.535533909	−2.61e-09	-0.000	reproduced
Octagons in a tan	4	s = 4+5/√2 = 7.53553+	7.535533909	−3.01e-09	-0.000	reproduced
Octagons in a tan	5	s = 9/2+3√2 = 8.74264+	8.742640780	−9.32e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	6	s = 4+7/√2 = 8.94974+	8.949747472	−3.58e-09	-0.000	reproduced
Octagons in a tan	7	s = 5+7/√2 = 9.94974+	9.949747652	−1.84e-07	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	8	s = 10.65684+	10.656854447	−1.44e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	9	s = 6+7/√2 = 10.94974+	11.363961257	−4.14e-01	-3.783	behind
Octagons in a tan	10	s = 5+9/√2 = 11.36396+	11.906285202	−5.42e-01	-4.772	behind
Octagons in a tan	11	s = 12.33328+	12.363961280	−3.07e-02	-0.249	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	12	s = 12.65684+	12.846804009	−1.90e-01	-1.501	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	13	s = 13.21750+	13.571070540	−3.54e-01	-2.675	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	14	s = 13/2+5√2 = 13.57106+	14.778177569	−1.2071	-8.895	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	15	s = 6+11/√2 = 13.77817+	14.778204160	−1.0000	-7.258	behind
Octagons in a tan	16	s = 8+9/√2 = 14.36396+	15.478050466	−1.1141	-7.756	behind
Octagons in a tan	17	s = 14.77816+	15.184706484	−4.07e-01	-2.751	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	18	s = 15.34720+	34.935230829	−19.5880	-127.633	behind	Found by Jonathan Viqueratl in May 2026.
Octagons in a tan	19	s = 15.68053+	17.065566455	−1.3850	-8.833	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	20	s = 15/2+6√2 = 15.98528+	17.596636166	−1.6114	-10.080	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a tan	21	s = 7+13/√2 = 16.19238+	34.935230829	−18.7428	-115.751	behind
Octagons in a tan	22	s = 16.77817+	18.202748862	−1.4246	-8.491	behind	Found by Thomas Greenleaf in June 2026.
Octagons in a triangle	2	s = 6.79962+	6.799624261	−4.26e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	3	s = (6+5√2+4√3+3√6)/4 = 6.83693+	6.836935073	−5.27e-09	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	4	s = 8.65211+	8.652115620	−5.62e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	5	s = 9.28498+	9.284990338	−1.03e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	6	s = 9.31576+	9.315773043	−1.30e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	7	s = 11.06632+	11.177640440	−1.11e-01	-1.006	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	8	s = 11.51025+	11.779907232	−2.70e-01	-2.343	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	9	s = 11.72998+	12.001531749	−2.72e-01	-2.315	behind
Octagons in a triangle	10	s = 11.80642+	11.810627333	−4.21e-03	-0.036	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	11	s = 13.24689+	14.261476677	−1.0146	-7.659	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	12	s = 13.62032+	14.261621109	−6.41e-01	-4.708	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a triangle	13	s = 14.04225+	14.287264062	−2.45e-01	-1.745	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	14	s = 14.23921+	14.299156560	−5.99e-02	-0.421	behind	Found by Aristotle Papowitz in July 2026.
Octagons in a triangle	15	s = 14.28169+	14.309446328	−2.78e-02	-0.194	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	16	s = 15.66136+	16.404486541	−7.43e-01	-4.745	behind	Found by Jonathan Viquerat in May 2026.
Octagons in a triangle	17	s = 16.06191+	16.240949402	−1.79e-01	-1.115	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a triangle	18	s = 16.40979+	16.853047798	−4.43e-01	-2.701	behind	Found by Aristotle Papowitz in July 2026.
Octagons in a triangle	19	s = 16.54447+	20.439650221	−3.8952	-23.544	behind	Found by Timo Berthold et al in May 2026.
Octagons in a triangle	20	s = 16.74196+	27.465822954	−10.7239	-64.054	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a triangle	21	s = 16.78582+	27.465822954	−10.6800	-63.625	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a triangle	22	s = 17.96238+	19.968168124	−2.0058	-11.167	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in a triangle	23	s = 18.39413+	27.465822954	−9.0717	-49.318	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a triangle	24	s = 18.55975+	29.091064542	−10.5313	-56.743	behind	Found by Jonathan Viquerat in August 2026.
Octagons in a triangle	25	s = 18.94531+	19.291018707	−3.46e-01	-1.825	behind	Found by Jonathan Viquerat in August 2026.
Octagons in an L	2	s = 1+√2 = 2.41421+	2.414213567	−4.56e-09	-0.000	reproduced
Octagons in an L	3	s = 1+√2 = 2.41421+	2.414213563	−9.66e-10	-0.000	reproduced
Octagons in an L	4	s = 3/2+5√2/4 = 3.26776+	3.503437867	−2.36e-01	-7.212	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	7	s = 2+3/√2 = 4.12132+	4.287435040	−1.66e-01	-4.031	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	8	s = 4.36459+	4.474873822	−1.10e-01	-2.527	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	9	s = 4.46274+	4.828427227	−3.66e-01	-8.194	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	10	s = 4.69035+	4.828427221	−1.38e-01	-2.944	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	11	s = 2+2√2 = 4.82842+	4.828427929	−8.04e-07	-0.000	reproduced
Octagons in an L	12	s = 2+2√2 = 4.82842+	4.828427221	−9.60e-08	-0.000	reproduced
Octagons in an L	13	s = 5.41620+	5.927883428	−5.12e-01	-9.447	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	14	s = 8/3+2√2 = 5.49509+	5.937345614	−4.42e-01	-8.048	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	15	s = 5.82002+	7.242640842	−1.4226	-24.444	behind	Found by Haowei Lin in June 2026.
Octagons in an L	16	s = 5.93197+	9.303462209	−3.3715	-56.836	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	17	s = 6.10747+	6.564593698	−4.57e-01	-7.485	behind	Found by Jonathan Viquerat in June 2026.
Octagons in an L	18	s = 6.25520+	6.613749814	−3.59e-01	-5.732	behind	Found by Vasily (Kotomord) Stolbov in September 2026.
Octagons in an L	19	s = 6.39782+	7.160283241	−7.62e-01	-11.918	behind	Found by Vasily (Kotomord) Stolbov in September 2026.
Octagons in an L	20	s = 6.51126+	13.699244226	−7.1880	-110.393	behind	Found by Vasily (Kotomord) Stolbov in September 2026.
Octagons in an octagon	2	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Octagons in an octagon	3	s = 5–2√2 = 2.17157+	2.171572876	−8.69e-10	-0.000	reproduced	Found by Ignacio Vallejo in March 2026.
Octagons in an octagon	4	s = √(5+1/√2) = 2.38895+	2.388955202	−3.72e-08	-0.000	reproduced	Found by Ignacio Vallejo in March 2026.
Octagons in an octagon	5	s = 2+1/√2 = 2.70710+	2.707106825	−4.40e-08	-0.000	reproduced	Found by Ignacio Vallejo in March 2026.
Octagons in an octagon	6	s = 2.98894+	2.997933773	−8.99e-03	-0.301	behind	Found by Nicolas Campailla in May 2026.
Octagons in an octagon	7	s = 3	3.000000001	−1.44e-09	-0.000	reproduced
Octagons in an octagon	8	s = 3.27524+	3.275244129	−4.13e-06	-0.000	reproduced	Found by Grant Mowry in May 2026.
Octagons in an octagon	9	s = 2+√2 = 3.41421+	3.414213622	−5.96e-08	-0.000	reproduced	Found by Ignacio Vallejo in March 2026.
Octagons in an octagon	10	s = 3+1/√2 = 3.70710+	3.707106847	−6.59e-08	-0.000	reproduced	Found by Ignacio Vallejo in March 2026.
Octagons in an octagon	11	s = 3.93256+	3.980786892	−4.82e-02	-1.226	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	12	s = 4	4.017095361	−1.71e-02	-0.427	behind
Octagons in an octagon	13	s = 7–2√2 = 4.17157+	4.279793257	−1.08e-01	-2.594	behind	Found by Ignacio Vallejo in March 2026.
Octagons in an octagon	14	s = 4.28135+	4.356364492	−7.50e-02	-1.752	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	15	s = 4.45584+	4.535533999	−7.97e-02	-1.789	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	16	s = 4.59803+	4.823898958	−2.26e-01	-4.912	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	17	s = 4.75690+	4.804523923	−4.76e-02	-1.001	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	18	s = 4.85681+	4.971358882	−1.15e-01	-2.359	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	19	s = 4.93550+	5.154315329	−2.19e-01	-4.433	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	20	s = 5.06727+	5.365161082	−2.98e-01	-5.879	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	21	s = 5.19695+	5.405373951	−2.08e-01	-4.011	behind	Found by Timo Berthold et al in May 2026.
Octagons in an octagon	22	s = 5.35686+	6.986502057	−1.6296	-30.422	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in an octagon	23	s = 4+√2 = 5.41421+	6.986502057	−1.5723	-29.040	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in an octagon	24	s = 5.55414+	5.920904169	−3.67e-01	-6.603	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in an octagon	25	s = 5.65411+	5.850001134	−1.96e-01	-3.465	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in an octagon	26	s = 5.73828+	6.015653929	−2.77e-01	-4.834	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in an octagon	27	s = 5.81167+	6.151576447	−3.40e-01	-5.849	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in an octagon	28	s = 3+2√2 = 5.82842+	6.144723806	−3.16e-01	-5.427	behind	Found by Ignacio Vallejo in March 2026.
Octagons in an octagon	29	s = 6.05649+	6.941732553	−8.85e-01	-14.616	behind	Found by Bhavithran Ananthan in July 2026.
Octagons in an octagon	30	s = 6.15306+	6.560998383	−4.08e-01	-6.630	behind	Found by Timo Berthold et al in May 2026.
Pentagons in a circle	2	r = √(5+2√5)/2 = 1.53884+	1.538841777	−8.58e-09	-0.000	reproduced
Pentagons in a circle	3	r = (1+√5)/2 = 1.61803+	1.618033989	−6.48e-10	-0.000	reproduced
Pentagons in a circle	4	r = 1.82971+	1.829715501	−5.50e-06	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a circle	5	r = 2.03271+	2.227032764	−1.94e-01	-9.560	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a circle	6	r = √((25+11√5)/10) = 2.22703+	2.227032761	−3.20e-08	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a circle	7	r = 2.29470+	2.294709904	−9.90e-06	-0.000	reproduced	Found by Jake Loyd in June 2026.
Pentagons in a circle	8	r = 2.48128+	2.481280615	−6.15e-07	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a circle	9	r = 2.70169+	2.702506269	−8.16e-04	-0.030	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	10	r = 2.79768+	2.817810169	−2.01e-02	-0.720	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a circle	11	r = 2.90171+	2.923890005	−2.22e-02	-0.764	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	12	r = 3.01808+	3.035050160	−1.70e-02	-0.562	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	13	r = 3.07768+	3.095629473	−1.79e-02	-0.583	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	14	r = 3.23377+	3.235799527	−2.03e-03	-0.063	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in a circle	15	r = 3.33877+	3.338774038	−4.04e-06	-0.000	reproduced	Found by Jake Loyd in June 2026.
Pentagons in a circle	16	r = 3.43657+	3.554790357	−1.18e-01	-3.440	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a circle	17	r = 3.50888+	3.615079886	−1.06e-01	-3.027	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	18	r = 3.61619+	3.682828879	−6.66e-02	-1.843	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	19	r = 3.67189+	3.840089781	−1.68e-01	-4.581	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	20	r = 3.80052+	4.646506761	−8.46e-01	-22.260	behind	Found by Jake Loyd in June 2026.
Pentagons in a circle	21	r = 3.90693+	4.082108376	−1.75e-01	-4.484	behind	Found by Haowei Lin in July 2026.
Pentagons in a circle	22	r = 3.99781+	5.670067425	−1.6723	-41.829	behind	Found by Haowei Lin in July 2026.
Pentagons in a circle	23	r = 4.07193+	4.248402715	−1.76e-01	-4.334	behind	Found by Haowei Lin in July 2026.
Pentagons in a circle	24	r = 4.12402+	4.319317338	−1.95e-01	-4.736	behind	Found by Haowei Lin in July 2026.
Pentagons in a circle	25	r = 4.23945+	4.475236285	−2.36e-01	-5.562	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a domino	2	s = 1.55460+	1.554603919	−3.92e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	3	s = 2.10051+	2.100514157	−4.16e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	4	s = 2.33739+	2.337395579	−5.58e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	5	s = 2.47315+	2.473151364	−1.36e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	6	s = 2.69228+	2.692281362	−1.36e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	7	s = 2.91977+	2.919770575	−5.75e-07	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	8	s = 3.07696+	3.160694627	−8.37e-02	-2.721	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	9	s = 3.33456+	3.431575952	−9.70e-02	-2.909	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	10	s = 3.51930+	3.535189097	−1.59e-02	-0.451	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a domino	11	s = 3.61313+	3.813880970	−2.01e-01	-5.556	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	12	s = 3.74837+	3.801336404	−5.30e-02	-1.413	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	13	s = 3.88151+	3.916079078	−3.46e-02	-0.891	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a domino	14	s = 3.92746+	3.946367220	−1.89e-02	-0.481	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	15	s = 4.11731+	4.275017555	−1.58e-01	-3.830	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a domino	16	s = 4.27934+	4.522753885	−2.43e-01	-5.688	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a domino	17	s = 4.38233+	8.432749283	−4.0504	-92.426	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a domino	18	s = 4.54032+	4.775857434	−2.36e-01	-5.188	behind	Found by Thomas Greenleaf in June 2026.
Pentagons in a domino	19	s = 4.67483+	4.821132698	−1.46e-01	-3.130	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a domino	20	s = 4.79125+	5.154211483	−3.63e-01	-7.576	behind	Found by Thomas Greenleaf in June 2026.
Pentagons in a domino	21	s = 4.87601+	8.483876059	−3.6079	-73.992	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a domino	22	s = 4.93220+	8.502638500	−3.5704	-72.390	behind	Found by Thomas Greenleaf in June 2026.
Pentagons in a domino	23	s = 5.01785+	8.518344270	−3.5005	-69.761	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a domino	24	s = 5.07794+	8.531684071	−3.4537	-68.015	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a domino	25	s = 5.22623+	5.366525543	−1.40e-01	-2.684	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a hexagon	2	s = 1.53879+	1.538841787	−5.18e-05	-0.003	behind
Pentagons in a hexagon	3	s = 1.73240+	1.732454671	−5.47e-05	-0.003	behind
Pentagons in a hexagon	4	s = 1.97666+	1.976689323	−2.93e-05	-0.001	behind	Found by Ethan Riddle in May 2026.
Pentagons in a hexagon	5	s = 2.21822+	2.311103654	−9.29e-02	-4.187	behind	Found by Nicolas Campailla in May 2026.
Pentagons in a hexagon	6	s = 2.32293+	2.322939333	−9.33e-06	-0.000	reproduced	Found by Bhavithran Ananthan in July 2026.
Pentagons in a hexagon	7	s = (2√5–1+√(15–6√5))/2 s = 2.36527+	2.365272305	−4.18e-08	-0.000	reproduced	Found by Nicolas Campailla in May 2026.
Pentagons in a hexagon	8	s = 2.71922+	2.719228626	−8.63e-06	-0.000	reproduced	Found by Bhavithran Ananthan in July 2026.
Pentagons in a hexagon	9	s = 2.86967+	2.921189920	−5.15e-02	-1.795	behind	Found by Nicolas Campailla in May 2026.
Pentagons in a hexagon	10	s = 2.93664+	2.938528126	−1.89e-03	-0.064	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a hexagon	11	s = 3.16125+	3.176436640	−1.52e-02	-0.480	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a hexagon	12	s = 3.21458+	3.229325424	−1.47e-02	-0.459	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	13	s = 3.40902+	3.455629679	−4.66e-02	-1.367	behind	Found by Nicolas Campailla in August 2026.
Pentagons in a hexagon	14	s = 3.46643+	3.494515011	−2.81e-02	-0.810	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a hexagon	15	s = 3.63499+	3.666299532	−3.13e-02	-0.861	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	16	s = 3.69895+	3.802266493	−1.03e-01	-2.793	behind	Found by Nicolas Campailla in August 2026.
Pentagons in a hexagon	17	s = 3.75774+	3.846517982	−8.88e-02	-2.363	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a hexagon	18	s = 3.84479+	3.879170594	−3.44e-02	-0.894	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	19	s = 3.88271+	4.166761761	−2.84e-01	-7.316	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a hexagon	20	s = 4.14048+	4.170696490	−3.02e-02	-0.730	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	21	s = 4.24003+	4.429786226	−1.90e-01	-4.475	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	22	s = 4.32443+	5.769344902	−1.4449	-33.413	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	23	s = 4.39703+	5.451509676	−1.0545	-23.982	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	24	s = 4.46360+	6.127887730	−1.6643	-37.286	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	25	s = 4.57861+	4.923832573	−3.45e-01	-7.540	behind	Found by Jake Loyd in June 2026.
Pentagons in a hexagon	26	s = 4.66031+	5.303365391	−6.43e-01	-13.799	behind	Found by Aristotle Papowitz in July 2026.
Pentagons in a hexagon	27	s = 4.71710+	5.112705422	−3.96e-01	-8.387	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a hexagon	28	s = 4.84364+	5.166415017	−3.23e-01	-6.664	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a hexagon	29	s = 4.91003+	5.327944222	−4.18e-01	-8.511	behind	Found by Aristotle Papowitz in July 2026.
Pentagons in a hexagon	30	s = 4.96406+	5.379122700	−4.15e-01	-8.361	behind	Found by Aristotle Papowitz in July 2026.
Pentagons in a hexagon	31	s = 5.09223+	5.712398041	−6.20e-01	-12.179	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a pentagon	2	s = 2	2.000000009	−8.58e-09	-0.000	reproduced
Pentagons in a pentagon	3	s = √5 = 2.23606+	2.236067978	−8.94e-10	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	4	s = 2.44719+	2.447213637	−2.36e-05	-0.001	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	5	s = (3+√5)/2 = 2.61803+	2.618034034	−4.49e-08	-0.000	reproduced
Pentagons in a pentagon	6	s = (3+√5)/2 = 2.61803+	2.618034004	−1.50e-08	-0.000	reproduced
Pentagons in a pentagon	7	s = 3.07866+	3.078689381	−2.94e-05	-0.001	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	8	s = 3.33514+	3.335174397	−3.44e-05	-0.001	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	9	s = 3.44956+	3.591143759	−1.42e-01	-4.104	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	10	s = 3.68324+	3.782754755	−9.95e-02	-2.702	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	11	s = 3.79704+	3.949601107	−1.53e-01	-4.018	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	12	s = 3.96926+	4.018778655	−4.95e-02	-1.248	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	13	s = 4.06523+	4.083045416	−1.78e-02	-0.438	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	14	s = 4.21111+	4.413828093	−2.03e-01	-4.814	behind	Found by Grant Mowry in May 2026.
Pentagons in a pentagon	15	s = 2+√5 = 4.23606+	4.539987919	−3.04e-01	-7.175	behind
Pentagons in a pentagon	16	s = 4.41636+	4.802456230	−3.86e-01	-8.742	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	17	s = 4.65536+	4.777558194	−1.22e-01	-2.625	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a pentagon	18	s = 4.77541+	5.013312895	−2.38e-01	-4.982	behind	Found by Jonathan Viquerat in April 2026.
Pentagons in a pentagon	19	s = 4.95267+	5.043914008	−9.12e-02	-1.842	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a pentagon	20	s = 5.03404+	7.717774365	−2.6837	-53.312	behind	Found by Jake Loyd in June 2026.
Pentagons in a pentagon	21	s = 5.15638+	5.237391637	−8.10e-02	-1.571	behind	Found by Jake Loyd in June 2026.
Pentagons in a pentagon	22	s = 5.26645+	7.717774365	−2.4513	-46.546	behind	Found by Grant Mowry in May 2026.
Pentagons in a pentagon	23	s = 5.34696+	7.717774365	−2.3708	-44.339	behind	Found by Jake Loyd in June 2026.
Pentagons in a pentagon	24	s = 5.49109+	7.717774365	−2.2267	-40.551	behind	Found by Jake Loyd in June 2026.
Pentagons in a pentagon	25	s = 5.58099+	6.453685047	−8.73e-01	-15.637	behind	Found by Jake Loyd in June 2026.
Pentagons in a pentagon	26	s = 5.67207+	7.273174149	−1.6011	-28.228	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a pentagon	27	s = 5.75528+	8.688385620	−2.9331	-50.964	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a pentagon	28	s = 5.84493+	8.694969587	−2.8500	-48.761	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a pentagon	29	s = 5.91835+	6.609949695	−6.92e-01	-11.686	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a square	2	s = (1+√5)[√(250+110√5) – 5(1+√5)]/8 s = 2.46345+	2.463451666	−1.45e-08	-0.000	reproduced
Pentagons in a square	3	s = (4+5√5/2)√(5+2√5)–55/4–23√5/4 s = 2.90811+	2.908117286	−1.73e-09	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a square	4	s = ((3–√5)√(5–√5)+7√10+√2)/8 s = 3.10252+	3.102525061	−4.94e-08	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a square	5	s = 3.54903+	3.549034820	−4.82e-06	-0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a square	6	s = 3.88299+	3.882991496	−1.50e-06	-0.000	reproduced	Found by Haowei Lin in July 2026.
Pentagons in a square	7	s = 4.18037+	4.180370664	−6.64e-07	-0.000	reproduced	Found by Nicolas Campailla in May 2026.
Pentagons in a square	8	s = 4.38190+	4.443850295	−6.20e-02	-1.414	behind	Found by Aristotle Papowitz in July 2026.
Pentagons in a square	9	s = 4.60033+	4.600329612	+3.88e-07	0.000	reproduced	Found by Jonathan Viquerat in April 2026.
Pentagons in a square	10	s = 4.90581+	4.978678326	−7.29e-02	-1.485	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in a square	11	s = 5.11555+	5.170365467	−5.48e-02	-1.072	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a square	12	s = 5.23221+	5.232214467	−4.47e-06	-0.000	reproduced	Found by Timo Berthold et al in May 2026.
Pentagons in a square	13	s = 5.52102+	5.525524355	−4.50e-03	-0.082	behind	Found by Jake Loyd in June 2026.
Pentagons in a square	14	s = 5.69659+	5.801342589	−1.05e-01	-1.839	behind	Found by Jake Loyd in June 2026.
Pentagons in a square	15	s = 5.90118+	5.981050805	−7.99e-02	-1.353	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a square	16	s = 6.06452+	6.179183983	−1.15e-01	-1.891	behind	Found by Timo Berthold et al in April 2026.
Pentagons in a square	17	s = 6.23761+	6.313322029	−7.57e-02	-1.214	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in a square	18	s = 6.32565+	6.570097345	−2.44e-01	-3.864	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a square	19	s = 6.55781+	6.732360030	−1.75e-01	-2.662	behind	Found by Jake Loyd in June 2026.
Pentagons in a square	20	s = 6.66135+	6.984082098	−3.23e-01	-4.845	behind	Found by Haowei Lin in July 2026.
Pentagons in a square	21	s = 6.85368+	7.080316523	−2.27e-01	-3.307	behind	Found by Jake Loyd in June 2026.
Pentagons in a square	22	s = 7.04445+	10.966797870	−3.9223	-55.680	behind	Found by Haowei Lin in July 2026.
Pentagons in a square	23	s = 7.20624+	7.894671661	−6.88e-01	-9.553	behind	Found by Jake Loyd in June 2026.
Pentagons in a square	24	s = 7.33690+	10.966797870	−3.6299	-49.475	behind	Found by Jake Loyd in June 2026.
Pentagons in a square	25	s = 7.45360+	8.229237071	−7.76e-01	-10.406	behind	Found by Jake Loyd in June 2026.
Pentagons in a square	26	s = 7.58176+	9.191709275	−1.6099	-21.235	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a square	27	s = 7.67948+	9.186856248	−1.5074	-19.629	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a square	28	s = 7.82010+	8.744212591	−9.24e-01	-11.817	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a square	29	s = 7.98512+	9.302064544	−1.3169	-16.492	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a square	30	s = 8.10222+	10.482071961	−2.3799	-29.373	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a tan	2	s = 3.52014+	3.520147038	−7.04e-06	-0.000	reproduced
Pentagons in a tan	3	s = 3.97792+	3.977926918	−6.92e-06	-0.000	reproduced
Pentagons in a tan	4	s = 4.63338+	4.633390129	−1.01e-05	-0.000	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	5	s = 5.16518+	5.165184087	−4.09e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	6	s = 5.48233+	5.482338720	−8.72e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	7	s = 6.03679+	6.072389305	−3.56e-02	-0.590	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	8	s = 6.30671+	6.342233339	−3.55e-02	-0.563	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	9	s = 6.69536+	6.730541821	−3.52e-02	-0.525	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	10	s = 6.98078+	7.047215393	−6.64e-02	-0.952	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	11	s = 7.34729+	7.523074272	−1.76e-01	-2.393	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	12	s = 7.54006+	7.730059955	−1.90e-01	-2.520	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	13	s = 7.82906+	7.952175507	−1.23e-01	-1.573	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	14	s = 8.16828+	8.255787201	−8.75e-02	-1.071	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a tan	15	s = 8.45706+	8.529414409	−7.24e-02	-0.856	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a tan	16	s = 8.66023+	8.805987901	−1.46e-01	-1.683	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a tan	17	s = 8.89679+	9.491393754	−5.95e-01	-6.683	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a tan	18	s = 9.08713+	9.624271067	−5.37e-01	-5.911	behind	Found by Jonathan Viqueratl in May 2026.
Pentagons in a tan	19	s = 9.38489+	10.195674027	−8.11e-01	-8.639	behind	Found by Thomas Greenleaf in June 2026.
Pentagons in a tan	20	s = 9.61296+	10.338014736	−7.25e-01	-7.542	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a tan	21	s = 9.79121+	19.717126462	−9.9259	-101.376	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a tan	22	s = 10.01063+	19.717126462	−9.7065	-96.962	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a tan	23	s = 10.24859+	19.717126462	−9.4685	-92.389	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a tan	24	s = 10.45171+	19.717126462	−9.2654	-88.650	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a tan	25	s = 10.63197+	13.873660033	−3.2417	-30.490	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in a triangle	3	s = √((75+33√5)/8) – (3–√5)/4 = 4.12164+	4.121647331	−1.75e-09	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	4	s = 5.21983+	5.219832877	−2.88e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	5	s = 5.55809+	5.558094107	−4.11e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	6	s = 5.63540+	5.635408351	−8.35e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	7	s = 6.50034+	6.500348494	−8.49e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	8	s = 6.81133+	6.811339286	−9.29e-06	-0.000	reproduced	Found by Bhavithran Ananthan in July 2026.
Pentagons in a triangle	9	s = 7.08969+	7.133094462	−4.34e-02	-0.612	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a triangle	10	s = 7.17235+	7.172357541	−7.54e-06	-0.000	reproduced	Found by Bhavithran Ananthan in July 2026.
Pentagons in a triangle	11	s = 7.93748+	7.959111515	−2.16e-02	-0.273	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	12	s = 8.19117+	8.474290913	−2.83e-01	-3.456	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	13	s = 8.37807+	8.544965750	−1.67e-01	-1.992	behind	Found by Jonathan Viquerat in May 2026.
Pentagons in a triangle	14	s = 8.58917+	8.642812512	−5.36e-02	-0.625	behind	Found by Haowei Lin in July 2026.
Pentagons in a triangle	15	s = 8.69161+	8.712807970	−2.12e-02	-0.244	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	16	s = 9.29700+	9.438377237	−1.41e-01	-1.521	behind	Found by Haowei Lin in July 2026.
Pentagons in a triangle	17	s = 9.57797+	9.852252635	−2.74e-01	-2.864	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	18	s = 9.78077+	10.054139988	−2.73e-01	-2.795	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	19	s = 9.92567+	16.530145775	−6.6045	-66.539	behind	Found by Haowei Lin in July 2026.
Pentagons in a triangle	20	s = 10.09879+	16.530145775	−6.4314	-63.684	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	21	s = 10.17148+	16.530145775	−6.3587	-62.515	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a triangle	22	s = 10.75818+	16.530145775	−5.7720	-53.652	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	23	s = 10.99100+	11.893544729	−9.03e-01	-8.212	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	24	s = 11.17511+	19.664495040	−8.4894	-75.967	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	25	s = 11.32392+	12.426616006	−1.1027	-9.738	behind	Found by Jake Loyd in June 2026.
Pentagons in a triangle	26	s = 11.45549+	12.056096182	−6.01e-01	-5.243	behind	Found by Aristotle Papowitz in July 2026.
Pentagons in a triangle	27	s = 11.59873+	13.051042810	−1.4523	-12.521	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a triangle	28	s = 11.69225+	13.208622141	−1.5164	-12.969	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a triangle	29	s = 12.18197+	13.612139276	−1.4302	-11.740	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a triangle	30	s = 12.38240+	13.962520373	−1.5801	-12.761	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	31	s = 12.58207+	13.921156539	−1.3391	-10.643	behind	Found by Jonathan Viquerat in August 2026.
Pentagons in a triangle	32	s = 12.70492+	13.966965423	−1.2620	-9.934	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	33	s = 12.85985+	13.648801527	−7.89e-01	-6.135	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	34	s = 12.97563+	14.301292700	−1.3257	-10.217	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	35	s = 13.10941+	14.616679009	−1.5073	-11.498	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in a triangle	36	s = 13.17841++	15.170206804	−1.9918	-15.114	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	37	s = 13.63430+	14.786463246	−1.1522	-8.450	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	38	s = 13.82313+	15.593920978	−1.7708	-12.810	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	39	s = 13.97521+	15.548895763	−1.5737	-11.261	behind	Found by Yue Huang in August 2026.
Pentagons in a triangle	40	s = 14.13674+	15.278384437	−1.1416	-8.076	behind	Found by Yue Huang in August 2026.
Pentagons in an L	2	s = √(5+2√5)/2 = 1.53884+	1.538841769	−6.16e-10	-0.000	reproduced
Pentagons in an L	3	s = 1.55425+	1.554247563	+2.44e-06	0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	4	s = 1.96918+	1.969181031	−1.03e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	5	s = 2.12433+	2.124337268	−7.27e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	6	s = 2.30512+	2.305121415	−1.42e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	7	s = 2.41732+	2.512760194	−9.54e-02	-3.948	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	8	s = 2.54164+	2.619379106	−7.77e-02	-3.059	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	9	s = 2.67860+	2.740633001	−6.20e-02	-2.316	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	10	s = 2.80245+	2.869649396	−6.72e-02	-2.398	behind
Pentagons in an L	11	s = 2.94662+	3.105638781	−1.59e-01	-5.397	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	12	s = 3.07460+	3.089182769	−1.46e-02	-0.474	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	13	s = 3.22359+	3.255496629	−3.19e-02	-0.990	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	14	s = 3.35014+	3.385783926	−3.56e-02	-1.064	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	15	s = 3.46668+	3.622656372	−1.56e-01	-4.499	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	16	s = 3.55643+	3.614731015	−5.83e-02	-1.639	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	17	s = 3.61458+	3.974472979	−3.60e-01	-9.957	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	18	s = 3.73452+	8.762569663	−5.0280	-134.637	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	19	s = 3.81113+	4.021478990	−2.10e-01	-5.519	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	20	s = 3.86901+	4.066635600	−1.98e-01	-5.108	behind	Found by Jonathan Viquerat in June 2026.
Pentagons in an L	21	s = 3.95816+	8.783790786	−4.8256	-121.916	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	22	s = 4.02153+	8.787287922	−4.7658	-118.506	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	23	s = 4.13155+	8.803226407	−4.6717	-113.073	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an L	24	s = 4.22847+	8.815292413	−4.5868	-108.475	behind	Found by Jonathan Viquerat in September 2026.
Pentagons in an octagon	2	s = 1.17774+	1.177778520	−3.85e-05	-0.003	behind
Pentagons in an octagon	3	s = 1.28954+	1.289544405	−4.40e-06	-0.000	reproduced	Found by Nicolas Campailla in May 2026.
Pentagons in an octagon	4	s = 1.42986+	1.429889758	−2.98e-05	-0.002	behind
Pentagons in an octagon	5	s = 1.61756+	1.617560353	−3.53e-07	-0.000	reproduced	Found by Nicolas Campailla in May 2026.
Pentagons in an octagon	6	s = 1.78003+	1.788113228	−8.08e-03	-0.454	behind	Found by Nicolas Campailla in May 2026.
Pentagons in an octagon	7	s = 1.82343+	1.823439320	−9.32e-06	-0.001	reproduced	Found by Timo Berthold et al in May 2026.
Pentagons in an octagon	8	s = 1.95989+	1.959891558	−1.56e-06	-0.000	reproduced	Found by Nicolas Campailla in May 2026.
Pentagons in an octagon	9	s = (√5+√(5+√5))/√(10–2√5) s = 2.09517+	2.095179356	−3.44e-08	-0.000	reproduced	Found by Nicolas Campailla in May 2026.
Pentagons in an octagon	10	s = 2.21135+	2.277240279	−6.59e-02	-2.980	behind	Found by Timo Berthold et al in May 2026.
Pentagons in an octagon	11	s = 2.33111+	2.383734184	−5.26e-02	-2.257	behind	Found by Timo Berthold et al in May 2026.
Pentagons in an octagon	12	s = 2.39327+	2.422515244	−2.92e-02	-1.222	behind	Found by Timo Berthold et al in May 2026.
Pentagons in an octagon	13	s = 2.49776+	2.538265310	−4.05e-02	-1.622	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	14	s = 2.56564+	2.612836079	−4.72e-02	-1.840	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	15	s = 2.68123+	2.689060999	−7.83e-03	-0.292	behind	Found by Timo Berthold et al in May 2026.
Pentagons in an octagon	16	s = 2.75249+	2.869677309	−1.17e-01	-4.258	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	17	s = 2.81043+	2.836476341	−2.60e-02	-0.927	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	18	s = 2.89321+	2.948363365	−5.52e-02	-1.906	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	19	s = 2.95527+	3.078022480	−1.23e-01	-4.154	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	20	s = 3.04679+	3.246234690	−1.99e-01	-6.546	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	21	s = 3.11874+	3.260526091	−1.42e-01	-4.546	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	22	s = 3.19144+	3.312652103	−1.21e-01	-3.798	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	23	s = 3.25129+	3.843371061	−5.92e-01	-18.211	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	24	s = 3.28718+	3.509203565	−2.22e-01	-6.754	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	25	s = 3.36617+	3.902518289	−5.36e-01	-15.933	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	26	s = 3.42775+	3.708592648	−2.81e-01	-8.193	behind	Found by Jake Loyd in June 2026.
Pentagons in an octagon	27	s = 3.49942+	3.894720691	−3.95e-01	-11.296	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in an octagon	28	s = 3.56402+	3.907029309	−3.43e-01	-9.624	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in an octagon	29	s = 3.61848+	4.019367250	−4.01e-01	-11.079	behind	Found by Bhavithran Ananthan in July 2026.
Pentagons in an octagon	30	s = 3.66678+	3.988821154	−3.22e-01	-8.783	behind	Found by Aristotle Papowitz in July 2026.
Pentagons in an octagon	31	s = 3.74379+	4.303808220	−5.60e-01	-14.959	behind	Found by Bhavithran Ananthan in July 2026.
Squares in a circle	3	r = 5 √17 / 16 = 1.288+	1.288470527	−1.89e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a circle	5	r = √10 / 2 = 1.581+	1.581138853	−2.24e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a circle	6	r = 1.688+*	1.688542998	−5.43e-04	-0.032	reproduced	Found by Erich Friedman in 1997.
Squares in a circle	7	r = √13 / 2 = 1.802+	1.802775669	−3.12e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a circle	8	r = 1.978+*	1.978770990	−7.71e-04	-0.039	reproduced	Found by David W. Cantrell in March 2002.
Squares in a circle	9	r = √1105 / 16 = 2.077+	2.121320408	−4.37e-02	-2.105	behind	Found by Erich Friedman in 1997.
Squares in a circle	10	r = 3 √2 / 2 = 2.121+	2.208297135	−8.70e-02	-4.101	behind	Found by Erich Friedman in 1997.
Squares in a circle	11	r = 2.21386+	2.359586326	−1.46e-01	-6.582	behind	Found by Milan Kovacic in May 2006.
Squares in a circle	12	r = √5 = 2.236+	2.336679587	−1.01e-01	-4.500	behind	Found by Erich Friedman in 1997.
Squares in a circle	13	r = 2.3607+	2.512383268	−1.52e-01	-6.425	behind	Found by David W. Cantrell in November 2010.
Squares in a circle	14	r = 2.5	2.508091226	−8.09e-03	-0.324	reproduced	Found by Erich Friedman in 1997.
Squares in a circle	15	r = 2.533+	2.674968817	−1.42e-01	-5.605	behind	Found by by David W. Cantrell in June 2002.
Squares in a circle	16	r = √11009 / 40 = 2.623+	2.828909388	−2.06e-01	-7.847	behind	Found by Erich Friedman in 1997.
Squares in a circle	17	r = 2.67687+	2.856899640	−1.80e-01	-6.725	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	18	r = √481 / 8 = 2.741+	3.027487624	−2.86e-01	-10.435	behind	Found by David W. Cantrell in March 2002.
Squares in a circle	19	r = 2.80150+	3.044280710	−2.43e-01	-8.666	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	20	r = 2.893+	3.040201117	−1.47e-01	-5.088	behind	Found by David W. Cantrell in June 2002.
Squares in a circle	21	r = √34 / 2 = 2.915+	3.250638188	−3.35e-01	-11.498	behind	Found by Erich Friedman in 1997.
Squares in a circle	22	r = 3.03239+	3.400178479	−3.68e-01	-12.129	behind	Found by Haowei Lin in July 2026.
Squares in a circle	23	r = 3.06738+	3.440948845	−3.74e-01	-12.179	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	24	r = 3.10940+	3.420800409	−3.11e-01	-10.015	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	25	r = 3.17450+	3.528772704	−3.54e-01	-11.160	behind	Found by Haowei Lin in July 2026.
Squares in a circle	26	r = √41 / 2 = 3.201+	3.523930776	−3.22e-01	-10.071	behind	Found by Erich Friedman in 1997.
Squares in a circle	27	r = 3.26050+	3.688896708	−4.28e-01	-13.139	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	28	r = 3.33147+	3.687820841	−3.56e-01	-10.697	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	29	r = 3.39309+	3.610453420	−2.17e-01	-6.406	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	30	r = 3.45962+	3.739730050	−2.80e-01	-8.097	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	31	r = 3.52771+	3.810344798	−2.83e-01	-8.012	behind	Found by Haowei Lin in July 2026.
Squares in a circle	32	r = 3.57340+	3.851151476	−2.78e-01	-7.773	behind	Found by Milan Kovacic in May 2026.
Squares in a circle	33	r = 3.60010+	3.875011081	−2.75e-01	-7.636	behind	Found by Haowei Lin in July 2026.
Squares in a circle	34	r = 3.62911+	4.007602464	−3.78e-01	-10.429	behind	Found by Jonathan Viquerat in August 2026.
Squares in a circle	35	r = √53 / 2 = 3.640+	4.109740443	−4.70e-01	-12.903	behind	Found by David Eppstein in March 2002.
Squares in a domino	2	s = 1	1.000000000	−4.00e-10	-0.000	reproduced
Squares in a domino	3	s = 3/2 = 1.5	1.500000024	−2.38e-08	-0.000	reproduced
Squares in a domino	4	s = 1.930+	1.930283346	−2.83e-04	-0.015	reproduced	Found by Evert Stenlund in June 2010.
Squares in a domino	5	s = 2	2.000000001	−8.21e-10	-0.000	reproduced
Squares in a domino	6	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Squares in a domino	7	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Squares in a domino	8	s = 2	2.000000025	−2.52e-08	-0.000	reproduced
Squares in a domino	9	s = 2 + √2/3 = 2.471+	2.471404565	−4.42e-08	-0.000	reproduced	Found by Evert Stenlund in June 2010.
Squares in a domino	10	s = 5/2 = 2.5	2.500000340	−3.40e-07	-0.000	reproduced
Squares in a domino	11	s = 2.779+	3.000000061	−2.21e-01	-7.953	behind	Found by Evert Stenlund in June 2010.
Squares in a domino	12	s = 6 (1 + √2) / 5 = 2.897+	3.000000060	−1.03e-01	-3.553	behind	Found by Maurizio Morandi in June 2010.
Squares in a domino	13	s = 2.976+	3.007198993	−3.12e-02	-1.048	behind	Found by David W. Cantrell in July 2012.
Squares in a domino	14	s = 3	3.000011766	−1.18e-05	-0.000	behind
Squares in a domino	15	s = 3	3.000000055	−5.46e-08	-0.000	reproduced
Squares in a domino	16	s = 3	3.354978039	−3.55e-01	-11.833	behind
Squares in a domino	17	s = 3	3.497274502	−4.97e-01	-16.576	behind
Squares in a domino	18	s = 3	3.612868233	−6.13e-01	-20.429	behind
Squares in a domino	19	s = 3 + 1/√5 = 3.447+	3.873237590	−4.26e-01	-12.359	behind	Found by Maurizio Morandi in June 2010.
Squares in a domino	20	s = 7/2 = 3.5	3.895919199	−3.96e-01	-11.312	behind
Squares in a domino	21	s = 7/2 = 3.5	7.343031958	−3.8430	-109.801	behind
Squares in a domino	22	s = 3.745+	7.343031958	−3.5980	-96.076	behind	Found by David W. Cantrell in July 2012.
Squares in a domino	23	s = 3.83525+	7.343031958	−3.5078	-91.462	behind	Found by Thomas Greenleaf in June 2026.
Squares in a domino	24	s = 3.88184+	4.047735135	−1.66e-01	-4.274	behind	Found by Aapo Lipponen in July 2026.
Squares in a domino	25	s = 3.939+	4.120793881	−1.82e-01	-4.615	behind	Found by David W. Cantrell in August 2012.
Squares in a domino	26	s = 3.98019+	4.035355700	−5.52e-02	-1.386	behind	Found by Aapo Lipponen in July 2026.
Squares in a domino	27	s = 4	4.076014168	−7.60e-02	-1.900	behind
Squares in a domino	28	s = 4	4.544857969	−5.45e-01	-13.621	behind
Squares in a domino	29	s = 4	4.540585724	−5.41e-01	-13.515	behind
Squares in a domino	30	s = 4	4.650379191	−6.50e-01	-16.259	behind
Squares in a domino	31	s = 4	4.760777856	−7.61e-01	-19.019	behind
Squares in a domino	32	s = 4	4.780391487	−7.80e-01	-19.510	behind
Squares in a domino	33	s = 3 + √2 = 4.414+	4.721045057	−3.07e-01	-6.951	behind	Found by Maurizio Morandi in July 2012.
Squares in a domino	34	s = 4 + √2/3 = 4.471+	5.036900156	−5.65e-01	-12.648	behind	Found by David W. Cantrell in July 2012.
Squares in a domino	35	s = 9/2 = 4.5	5.088845692	−5.89e-01	-13.085	behind
Squares in a domino	36	s = 9/2 = 4.5	5.068425370	−5.68e-01	-12.632	behind
Squares in a domino	37	s = 4.71758+	5.313415753	−5.96e-01	-12.630	behind	Found by Aapo Lipponen in July 2026.
Squares in a domino	38	s = 4.79816+	5.248570270	−4.50e-01	-9.387	behind
Squares in a domino	39	s = 4.83693+	5.295577275	−4.59e-01	-9.482	behind	Found by Aapo Lipponen in July 2026.
Squares in a domino	40	s = 4.895+	5.374392333	−4.79e-01	-9.794	behind	Found by Sigvart Brendberg in June 2023.
Squares in a domino	41	s = 4.927+	5.415173607	−4.88e-01	-9.908	behind	Found by Sigvart Brendberg in June 2023.
Squares in a domino	42	s = 4.96862+	5.309337294	−3.41e-01	-6.857	behind	Found by Aapo Lipponen in July 2026.
Squares in a domino	43	s = 5	5.502516840	−5.03e-01	-10.050	behind
Squares in a domino	44	s = 5	5.533545545	−5.34e-01	-10.671	behind
Squares in a domino	45	s = 5	5.852664544	−8.53e-01	-17.053	behind
Squares in a domino	46	s = 5	5.853853353	−8.54e-01	-17.077	behind
Squares in a domino	47	s = 5	5.924234907	−9.24e-01	-18.485	behind
Squares in a domino	48	s = 5	5.981237744	−9.81e-01	-19.625	behind
Squares in a domino	49	s = 5	6.068103914	−1.0681	-21.362	behind
Squares in a domino	50	s = 5	6.121493322	−1.1215	-22.430	behind
Squares in a hexagon	2	s = 2/√3 = 1.15470+	1.154700546	−7.53e-09	-0.000	reproduced
Squares in a hexagon	3	s = (1+√3)/2 = 1.36602+	1.366025431	−2.72e-08	-0.000	reproduced	Found by Maurizio Morandi in March 2026.
Squares in a hexagon	4	s = 2/3^(1/4) = 1.51967+	1.519671396	−2.47e-08	-0.000	reproduced	Found by Maurizio Morandi in March 2026.
Squares in a hexagon	5	s = √3 = 1.73205+	1.741632824	−9.58e-03	-0.553	behind
Squares in a hexagon	6	s = 1.821+	1.839593824	−1.86e-02	-1.021	behind	Found by Maurizio Morandi in March 2026.
Squares in a hexagon	7	s = (√2)3^(1/4) = 1.86120+	1.868423013	−7.21e-03	-0.388	behind	Found by Maurizio Morandi in March 2026.
Squares in a hexagon	8	s = 2.15378+	2.154700883	−9.21e-04	-0.043	behind	Found by Ian Watson in April 2026.
Squares in a hexagon	9	s = 1/2+√3 = 2.23205+	2.273624343	−4.16e-02	-1.863	behind	Found by Jonathan Viquerat in April 2026.
Squares in a hexagon	10	s = 4/√3 = 2.30940+	2.341434837	−3.20e-02	-1.387	behind
Squares in a hexagon	11	s = 2.40944+	2.415429081	−5.99e-03	-0.249	behind	Found by Jonathan Viquerat in April 2026.
Squares in a hexagon	12	s = 1+5√3/6 = 2.44337+	2.491391931	−4.80e-02	-1.965	behind	Found by Maurizio Morandi in March 2026.
Squares in a hexagon	13	s = 2.572+	2.612596729	−4.06e-02	-1.578	behind	Found by Maurizio Morandi in April 2026.
Squares in a hexagon	14	s = 2.62126+	2.720319168	−9.91e-02	-3.779	behind	Found by Jonathan Viquerat in April 2026.
Squares in a hexagon	15	s = 2.75364+	2.799353506	−4.57e-02	-1.660	behind	Found by Grant Mowry in May 2026.
Squares in a hexagon	16	s = 2.82002+	2.992282136	−1.72e-01	-6.109	behind	Found by Spencer Leach in May 2026.
Squares in a hexagon	17	s = 2.87264+	2.950900245	−7.83e-02	-2.724	behind	Found by Jake Loyd in May 2026.
Squares in a hexagon	18	s = 2.92104+	3.029493828	−1.08e-01	-3.713	behind	Found by Haowei Lin in July 2026.
Squares in a hexagon	19	s = 2.93508+	3.124125484	−1.89e-01	-6.441	behind	Found by Haowei Lin in July 2026.
Squares in a hexagon	20	s = 3.16122+	3.330649050	−1.69e-01	-5.360	behind	Found by Leo Strijbos in August 2026.
Squares in a hexagon	21	s = (23+11√3)/13 = 3.23481+	5.034022026	−1.7992	-55.620	behind	Found by Spencer Leach in May 2026.
Squares in a hexagon	22	s = 3.31432+	5.285634236	−1.9713	-59.479	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	23	s = 3.36407+	5.299725932	−1.9357	-57.539	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	24	s = 3.40286+	5.309783560	−1.9069	-56.039	behind	Found by Thomas Greenleaf in June 2026.
Squares in a hexagon	25	s = 2√3 = 3.46410+	3.833051535	−3.69e-01	-10.651	behind
Squares in a hexagon	26	s = 3.49276+	3.934975170	−4.42e-01	-12.661	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	27	s = (9+7√3)/6 = 3.52072+	3.757623327	−2.37e-01	-6.729	behind	Found by Erich Friedman in April 2026.
Squares in a hexagon	28	s = 3.61976+	3.909659518	−2.90e-01	-8.009	behind	Found by Leo Strijbos in August 2026.
Squares in a hexagon	29	s = 3.66437+	4.065400801	−4.01e-01	-10.944	behind	Found by Ian Watson in April 2026.
Squares in a hexagon	30	s = 3.69552+	3.957728174	−2.62e-01	-7.095	behind	Found by Aristotle Papowitz in July 2026.
Squares in a hexagon	31	s = 3.78143+	4.190876497	−4.09e-01	-10.828	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	32	s = 3.84140+	4.149326638	−3.08e-01	-8.016	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	33	s = 3.86634+	4.341110162	−4.75e-01	-12.280	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	34	s = 3.91853+	4.348919206	−4.30e-01	-10.983	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	35	s = 3.98201+	4.674599576	−6.93e-01	-17.393	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	36	s = 4.02042+	4.570728453	−5.50e-01	-13.688	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	37	s = 7/√3 = 4.04145+	4.741643845	−7.00e-01	-17.325	behind
Squares in a hexagon	38	s = 4.18035+	4.728360354	−5.48e-01	-13.109	behind	Found by Leo Strijbos in August 2026.
Squares in a hexagon	39	s = 4.24512+	4.723338060	−4.78e-01	-11.265	behind	Found by Jake Loyd in June 2026.
Squares in a hexagon	40	s = 4.30171+	4.874697951	−5.73e-01	-13.320	behind	Found by Aristotle Papowitz in July 2026.
Squares in a pentagon	2	s = 4√(1–2/√5)+√5–2 s = 1.535+	1.535746779	−1.68e-08	-0.000	reproduced	Found by Erich Friedman in March 2012.
Squares in a pentagon	3	s = 1.695+	1.695619534	−6.20e-04	-0.037	reproduced	Found by David W. Cantrell in July 2012.
Squares in a pentagon	4	s = 1.861+	1.861668600	−6.69e-04	-0.036	reproduced	Found by Maurizio Morandi in July 2012.
Squares in a pentagon	5	s = 1 + cos(18°) s = 1.951+	1.961492735	−1.05e-02	-0.538	behind	Found by Erich Friedman in March 2012.
Squares in a pentagon	6	s = 6√(1–2/√5)+√5–2 s = 2.185+	2.185586185	−2.99e-08	-0.000	reproduced	Found by Erich Friedman in March 2012.
Squares in a pentagon	7	s = 6√(1–2/√5)+2√5–4 s = 2.421+	2.439120215	−1.75e-02	-0.721	behind	Found by Erich Friedman in July 2012.
Squares in a pentagon	8	s = 2.565+	2.575452184	−1.05e-02	-0.407	behind	Found by David W. Cantrell in July 2012.
Squares in a pentagon	9	s = 2.693+	2.705412403	−1.24e-02	-0.461	behind	Found by Timo Berthold et al in January 2026.
Squares in a pentagon	10	s = 2.793+	2.865627336	−7.26e-02	-2.600	behind	Found by Timo Berthold et al in January 2026.
Squares in a pentagon	11	s = 2.890+	2.894847645	−4.85e-03	-0.168	behind	Found by Timo Berthold et al in January 2026.
Squares in a pentagon	12	s = 2.969+	2.988831879	−1.98e-02	-0.668	behind	Found by Timo Berthold et al in January 2026.
Squares in a pentagon	13	s = 3.12074+	3.261282990	−1.41e-01	-4.504	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	14	s = 3.187+	3.242672578	−5.57e-02	-1.747	behind	Found by David W. Cantrell in July 2012.
Squares in a pentagon	15	s = (√(125–38√5)+8–2√5)/3 s = 3.284+	3.491417618	−2.07e-01	-6.288	behind	Found by David W. Cantrell in July 2012.
Squares in a pentagon	16	s = 3.47851+	3.614753452	−1.36e-01	-3.917	behind	Found by Jonathan Viquerat in May 2026.
Squares in a pentagon	17	s = 3.541+	3.610575030	−6.96e-02	-1.965	behind	Found by Ignacio Vallejo in March 2026.
Squares in a pentagon	18	s = 3.62598+	6.583326252	−2.9573	-81.560	behind	Found by Haowei Lin in July 2026.
Squares in a pentagon	19	s = 3.70918+	3.752941896	−4.38e-02	-1.180	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	20	s = 3.79775+	4.104049640	−3.06e-01	-8.065	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	21	s = 3.86365+	6.583326252	−2.7197	-70.391	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	22	s = 3.93347+	4.286599420	−3.53e-01	-8.978	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	23	s = 4.00109+	4.288756054	−2.88e-01	-7.190	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	24	s = 4.10103+	6.583326252	−2.4823	-60.529	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	25	s = 4.16727+	6.583326252	−2.4161	-57.977	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	26	s = 4.22150+	4.689481890	−4.68e-01	-11.086	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	27	s = 4.34851+	4.992100511	−6.44e-01	-14.800	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	28	s = 4.41576+	4.856689998	−4.41e-01	-9.985	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	29	s = 4.49879+	5.932657950	−1.4339	-31.872	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	30	s = 4.54753+	4.963116963	−4.16e-01	-9.139	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	31	s = 4.62404+	5.274710839	−6.51e-01	-14.071	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	32	s = 4.70000+	5.933068522	−1.2331	-26.236	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	33	s = 4.75331+	5.195334344	−4.42e-01	-9.299	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	34	s = 4.81345+	5.398892797	−5.85e-01	-12.163	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	35	s = 4.86283+	5.938419837	−1.0756	-22.119	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	36	s = 4.93131+	6.420048294	−1.4887	-30.190	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	37	s = 4.97801+	5.576858874	−5.99e-01	-12.030	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	38	s = 5.04838+	5.616895818	−5.69e-01	-11.261	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	39	s = 5.13653+	5.914377651	−7.78e-01	-15.143	behind	Found by Jake Loyd in June 2026.
Squares in a pentagon	40	s = 5.16849+	5.966346430	−7.98e-01	-15.437	behind	Found by Jake Loyd in June 2026.
Squares in a tan	2	s = 2√2 = 2.828+	2.828427126	−1.13e-09	-0.000	reproduced
Squares in a tan	3	s = 3	3.000000001	−1.20e-09	-0.000	reproduced
Squares in a tan	4	s = 5 / √2 = 3.535	3.535533907	−1.41e-09	-0.000	reproduced	Found by Erich Friedman in March 2005.
Squares in a tan	5	s = 4	4.000000038	−3.75e-08	-0.000	reproduced	Found by Erich Friedman in March 2005.
Squares in a tan	6	s = 4	4.121320420	−1.21e-01	-3.033	behind
Squares in a tan	7	s = 3 + √2 = 4.414+	4.414213564	−2.09e-09	-0.000	reproduced	Found by Erich Friedman in March 2005.
Squares in a tan	8	s = 2 + 2√2 = 4.828+	4.828427216	−9.12e-08	-0.000	reproduced	Found by Erich Friedman in March 2005.
Squares in a tan	9	s = 7 / √2 = 4.949+	5.000000103	−5.03e-02	-1.015	behind	Found by Erich Friedman in March 2005.
Squares in a tan	10	s = 5	5.512478378	−5.12e-01	-10.250	behind
Squares in a tan	11	s = 4 + √2 = 5.414+	5.656963183	−2.43e-01	-4.484	behind	Found by Erich Friedman in March 2005.
Squares in a tan	12	s = 4√2 = 5.656+	5.656855022	−7.72e-07	-0.000	reproduced	Found by Erich Friedman in March 2005.
Squares in a tan	13	s = 3 + 2√2 = 5.828+	6.122480318	−2.94e-01	-5.046	behind	Found by Erich Friedman in March 2005.
Squares in a tan	14	s = 6	6.536789543	−5.37e-01	-8.946	behind	Found by Erich Friedman in March 2005.
Squares in a tan	15	s = 6	6.121320467	−1.21e-01	-2.022	behind
Squares in a tan	16	s = 9 / √2 = 6.363+	16.661738239	−10.2978	-161.838	behind	Found by Erich Friedman in March 2005.
Squares in a tan	17	s = 5 + √2 = 6.414+	7.251551045	−8.37e-01	-13.055	behind	Found by Erich Friedman in March 2005.
Squares in a tan	18	s = 4 + 2√2 = 6.828+	7.723499493	−8.95e-01	-13.109	behind	Found by Erich Friedman in March 2005.
Squares in a tan	19	s = 2 + 7 / √2 = 6.949+	7.863650851	−9.14e-01	-13.152	behind	Found by David W. Cantrell in May 2005.
Squares in a tan	20	s = 7	7.709095841	−7.09e-01	-10.130	behind	Found by Erich Friedman in March 2005.
Squares in a tan	21	s = 7	8.318821971	−1.3188	-18.840	behind
Squares in a tan	22	s = 1 + 9 / √2 = 7.363+	16.259865106	−8.8959	-120.819	behind	Found by Erich Friedman in March 2005.
Squares in a tan	23	s = 6 + √2 = 7.414+	16.259865106	−8.8457	-119.310	behind	Found by Erich Friedman in March 2005.
Squares in a tan	24	s = 7 + 1 / √2 = 7.707+	16.259865106	−8.5528	-110.974	behind	Found by David W. Cantrell in May 2005.
Squares in a tan	25	s = 11 / √2 = 7.778+	21.067557414	−13.2894	-170.859	behind
Squares in a tan	26	s = 5 + 2√2 = 7.828+	8.853700398	−1.0253	-13.098	behind	Found by Erich Friedman in March 2026.
Squares in a tan	27	s = 8	9.208774973	−1.2088	-15.110	behind	Inherited published construction at n=28; not a newly discovered record
Squares in a tan	28	s = 8	9.423131447	−1.4231	-17.789	behind
Squares in a triangle	2	s = 2 + 2 / √3 = 3.154+	3.154700556	−1.74e-08	-0.000	reproduced
Squares in a triangle	3	s = 3 / 2 + √3 = 3.232+	3.232050809	−1.31e-09	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a triangle	4	s = 3 + 2 / √3 = 4.154+	4.154700608	−6.95e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a triangle	5	s = 2 + 4 / √3 = 4.309+	4.309401143	−6.63e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a triangle	6	s = 2 + 4 / √3 = 4.309+	4.309401157	−8.00e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a triangle	7	s = 4 + 2 / √3 = 5.154+	5.154700631	−9.26e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Squares in a triangle	8	s = 5.301+	5.309401248	−8.40e-03	-0.158	behind	Found by David W. Cantrell in July 2002.
Squares in a triangle	9	s = 3 + 4 / √3 = 5.309+	5.463402074	−1.54e-01	-2.901	behind	Found by Erich Friedman in 1997.
Squares in a triangle	10	s = 2 + 2 √3 = 5.464+	6.232051386	−7.68e-01	-14.055	behind	Found by Erich Friedman in 1997.
Squares in a triangle	11	s = 5 + 2 / √3 = 6.154+	6.309401208	−1.55e-01	-2.514	behind	Found by Erich Friedman in 1997.
Squares in a triangle	12	s = 6.301+	6.464101816	−1.63e-01	-2.589	behind	Found by David W. Cantrell in July 2002.
Squares in a triangle	13	s = 4 + 4 / √3 = 6.309+	6.618803434	−3.09e-01	-4.904	behind	Found by Erich Friedman in 1997.
Squares in a triangle	14	s = 3 + 2 √3 = 6.464+	6.613959946	−1.50e-01	-2.318	behind	Found by Erich Friedman in 1997.
Squares in a triangle	15	s = 3 + 2 √3 = 6.464+	6.618802293	−1.55e-01	-2.393	behind	Found by Erich Friedman in 1997.
Squares in a triangle	16	s = 6 + 2 / √3 = 7.154+	7.369987609	−2.15e-01	-3.009	behind	Found by Erich Friedman in 1997.
Squares in a triangle	17	s = 7.301+	7.620162927	−3.19e-01	-4.371	behind	Found by David W. Cantrell in July 2002.
Squares in a triangle	18	s = 5 + 4 / √3 = 7.309+	7.622797190	−3.13e-01	-4.288	behind	Found by Erich Friedman in 1997.
Squares in a triangle	19	s = 4 + 2 √3 = 7.464+	7.880515081	−4.16e-01	-5.579	behind	Found by Erich Friedman in 1997.
Squares in a triangle	20	s = 7.61695+	13.128278314	−5.5113	-72.356	behind	Found by Haowei Lin in July 2026.
Squares in a triangle	21	s = 3 + 8 / √3 = 7.618+	13.128278314	−5.5095	-72.322	behind	Found by Erich Friedman in 1997.
Squares in a triangle	22	s = 7 + 2 / √3 = 8.15470+	13.128278314	−4.9736	-60.990	behind	Found by Erich Friedman in 1997.
Squares in a triangle	23	s = 8.301+	13.128278314	−4.8273	-58.153	behind	Found by David W. Cantrell in July 2002.
Squares in a triangle	24	s = 6 + 4 / √3 = 8.309+	17.025143002	−8.7157	-104.895	behind	Found by Erich Friedman in 1997.
Squares in a triangle	25	s = 5 + 2 √3 = 8.464+	9.052540520	−5.88e-01	-6.952	behind	Found by Erich Friedman in 1997.
Squares in a triangle	26	s = 4 + 8 / √3 = 8.618+	9.265104466	−6.46e-01	-7.499	behind	Found by Erich Friedman in 1997.
Squares in a triangle	27	s = 4 + 8 / √3 = 8.618+	9.356379872	−7.38e-01	-8.559	behind	Found by Erich Friedman in 1997.
Squares in a triangle	28	s = 3 + 10 / √3 = 8.773+	9.464203885	−6.91e-01	-7.873	behind	Found by Erich Friedman in 1997.
Squares in a triangle	29	s = 8 + 2 / √3 = 9.154+	10.216155138	−1.0615	-11.596	behind	Found by Erich Friedman in 1997.
Squares in a triangle	30	s = 9.301+	10.162391108	−8.61e-01	-9.261	behind	Found by David W. Cantrell in July 2002.
Squares in a triangle	31	s = 7 + 4 / √3 = 9.309+	10.390385314	−1.0810	-11.612	behind	Found by Erich Friedman in 1997.
Squares in a triangle	32	s = 6 + 2 √3 = 9.464+	10.024325937	−5.60e-01	-5.920	behind	Found by Erich Friedman in 1997.
Squares in a triangle	33	s = 5 + 8 / √3 = 9.618+	11.190298353	−1.5715	-16.339	behind	Found by Erich Friedman in 1997.
Squares in a triangle	34	s = 5 + 8 / √3 = 9.618+	10.832145023	−1.2133	-12.615	behind	Found by Erich Friedman in 1997.
Squares in a triangle	35	s = 4 + 10 / √3 = 9.773+	11.454642037	−1.6811	-17.202	behind	Found by Erich Friedman in 1997.
Squares in a triangle	36	s = 4 + 10 / √3 = 9.773+	11.151224928	−1.3777	-14.097	behind	Found by Erich Friedman in 1997.
Squares in a triangle	37	s = 10.15299+	11.454851438	−1.3019	-12.822	behind	Found by Gianluca Costantino in May 2026.
Squares in a triangle	38	s = 10.304+	11.500926965	−1.1969	-11.616	behind	Found by Gianluca Costantino in April 2026.
Squares in a triangle	39	s = 8 + 4 / √3 = 10.30940+	11.669029245	−1.3596	-13.188	behind	Found by Bhavithran Ananthan in July 2026.
Squares in a triangle	40	s = 7 + 2√3 = 10.46410+	12.485556719	−2.0215	-19.318	behind	Found by Bhavithran Ananthan in July 2026.
Squares in a triangle	41	s = 10.61880+	11.556218688	−9.37e-01	-8.828	behind	Found by Aristotle Papowitz in July 2026.
Squares in a triangle	42	s = 10.61880+	11.542436139	−9.24e-01	-8.698	behind	Found by Aristotle Papowitz in July 2026.
Squares in a triangle	43	s = 10.77350+	11.645366099	−8.72e-01	-8.093	behind	Found by Aristotle Papowitz in July 2026.
Squares in an L	2	s = 2	2.000000010	−9.59e-09	-0.000	reproduced
Squares in an L	3	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Squares in an L	4	s = 3	3.000000036	−3.65e-08	-0.000	reproduced
Squares in an L	5	s = 3	3.000000051	−5.10e-08	-0.000	reproduced
Squares in an L	6	s = (5√2 + 4) / 3 = 3.690+	3.691334552	−9.79e-04	-0.027	reproduced	Found by David W. Cantrell in June 2005.
Squares in an L	7	s = √2 + 5/2 = 3.914+	4.000000080	−8.58e-02	-2.192	behind	Found by Erich Friedman in June 2005.
Squares in an L	8	s = 4	4.000000061	−6.08e-08	-0.000	reproduced
Squares in an L	9	s = 4	4.000000073	−7.34e-08	-0.000	reproduced
Squares in an L	10	s = 4	4.000000070	−7.04e-08	-0.000	reproduced
Squares in an L	11	s = 4	4.000000070	−7.03e-08	-0.000	reproduced
Squares in an L	12	s = 4	4.000000701	−7.01e-07	-0.000	reproduced
Squares in an L	13	s = 2 + 2√2 = 4.828+	5.023689366	−1.95e-01	-4.044	behind	Found by Maurizio Morandi in October 2008.
Squares in an L	14	s = 4.98674+	5.414213670	−4.27e-01	-8.572	behind	Found by Jonathan Viquerat in June 2026.
Squares in an L	15	s = 5	6.000001234	−1.0000	-20.000	behind
Squares in an L	16	s = 5	7.647232682	−2.6472	-52.945	behind
Squares in an L	17	s = 4/3 + 3√2 = 5.575+	5.939978457	−3.64e-01	-6.529	behind	Found by Maurizio Morandi in October 2008.
Squares in an L	18	s = (2√2 + 14) / 3 = 5.609+	6.253259554	−6.44e-01	-11.478	behind	Found by Erich Friedman in June 2005.
Squares in an L	19	s = 5.792+	6.059383849	−2.67e-01	-4.616	behind	Found by David W. Cantrell in July 2012.
Squares in an L	20	s = 5.937+	14.686063917	−8.7491	-147.365	behind	Found by David W. Cantrell in July 2012.
Squares in an L	21	s = 6	14.686063917	−8.6861	-144.768	behind
Squares in an L	22	s = 6	14.686063917	−8.6861	-144.768	behind
Squares in an L	23	s = 6	14.686063917	−8.6861	-144.768	behind
Squares in an L	24	s = 6	14.686063917	−8.6861	-144.768	behind
Squares in an L	25	s = 6	6.902645979	−9.03e-01	-15.044	behind
Squares in an L	26	s = 6	7.057823410	−1.0578	-17.630	behind
Squares in an L	27	s = 6	7.234960298	−1.2350	-20.583	behind
Squares in an L	28	s = 6 + √2/2 = 6.707+	7.705632011	−9.99e-01	-14.888	behind	Found by Maurizio Morandi in September 2015.
Squares in an L	29	s = 6.840+	7.459934584	−6.20e-01	-9.063	behind	Found by Maurizio Morandi in September 2015.
Squares in an L	30	s = 7	7.374595604	−3.75e-01	-5.351	behind
Squares in an L	31	s = 7	8.039699898	−1.0397	-14.853	behind
Squares in an L	32	s = 7	8.121644973	−1.1216	-16.023	behind
Squares in an L	33	s = 7	8.204610056	−1.2046	-17.209	behind
Squares in an L	34	s = 7.513+	8.220003129	−7.07e-01	-9.410	behind	Found by Joe DeVincentis in September 2015.
Squares in an L	35	s = 7.55991+	8.246676914	−6.87e-01	-9.084	behind	Found by Aapo Lipponen in July 2026.
Squares in an L	36	s = 7.730+	8.376146804	−6.46e-01	-8.359	behind	Found by Joe DeVincentis in September 2015.
Squares in an octagon	2	s = √(6–√2–√(20√2–26))/2 = 0.87669+	0.876699201	−1.34e-08	-0.000	reproduced	Found by Maurizio Morandi in December 2013.
Squares in an octagon	3	s = 18 – 12√2 = 1.02943+	1.029437267	−1.59e-08	-0.000	reproduced	Found by Erich Friedman in December 2013.
Squares in an octagon	4	s = √(4–2√2) = 1.08239+	1.082392211	−1.02e-08	-0.000	reproduced
Squares in an octagon	5	s = 3√2 – 3 = 1.24264+	1.242640688	−1.35e-09	-0.000	reproduced
Squares in an octagon	6	s = 7 – 4√2 = 1.34314+	1.343145772	−2.10e-08	-0.000	reproduced	Found by Maurizio Morandi in December 2013.
Squares in an octagon	7	s = √(5–√2–√(8√2–9)) = 1.43690+	1.436905902	−2.33e-08	-0.000	reproduced	Found by Maurizio Morandi in December 2013.
Squares in an octagon	8	s = 1.56962+	1.573238002	−3.62e-03	-0.231	behind	Found by Grant Mowry in May 2026.
Squares in an octagon	9	s = 3/√(2+√2) = 1.62358+	1.623588361	−6.05e-08	-0.000	reproduced
Squares in an octagon	10	s = 1.68171+	1.729939339	−4.82e-02	-2.868	behind	Found by Timo Berthold et al in May 2026.
Squares in an octagon	11	s = 1.73152+	1.731585166	−6.52e-05	-0.004	behind	Found by Jonathan Viquerat in May 2026.
Squares in an octagon	12	s = √(6–√2–√(20√2–26)) = 1.75339+	1.878876685	−1.25e-01	-7.156	behind	Found by Maurizio Morandi in December 2013.
Squares in an octagon	13	s = 1.89674+	1.983946334	−8.72e-02	-4.598	behind	Found by Grant Mowry in May 2026.
Squares in an octagon	14	s = 1.98302+	2.024750387	−4.17e-02	-2.104	behind	Found by Timo Berthold et al in May 2026.
Squares in an octagon	15	s = 2.03168+	2.118912564	−8.72e-02	-4.294	behind	Found by Jonathan Viquerat in May 2026.
Squares in an octagon	16	s = 5√2 – 5 = 2.07106+	2.246165887	−1.75e-01	-8.455	behind
Squares in an octagon	17	s = 5√2 – 5 = 2.07106+	2.238750605	−1.68e-01	-8.096	behind
Squares in an octagon	18	s = 2.16732+	2.437207216	−2.70e-01	-12.453	behind	Found by Timo Berthold et al in May 2026.
Squares in an octagon	19	s = 2.22435+	2.552503830	−3.28e-01	-14.753	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	20	s = 2.28598+	2.552902430	−2.67e-01	-11.676	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	21	s = sqrt(48–9√2–3√(104√2–126))/2 = 2.31833+	3.339910071	−1.0216	-44.065	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	22	s = 2.41575+	2.726176767	−3.10e-01	-12.850	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	23	s = 2.46879+	2.738901592	−2.70e-01	-10.941	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	24	s = 6√2–6 = 2.48528+	2.735897494	−2.51e-01	-10.084	behind
Squares in an octagon	25	s = 17(2–√2)/4 = 2.48959+	2.711886033	−2.22e-01	-8.929	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	26	s = 2.52709+	2.740545092	−2.13e-01	-8.447	behind	Found by Aristotle Papowitz in July 2026.
Squares in an octagon	27	s = 2.58584+	2.979552732	−3.94e-01	-15.226	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	28	s = 2.62788+	2.892202881	−2.64e-01	-10.058	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	29	s = 2.70553+	3.032341274	−3.27e-01	-12.079	behind	Found by Jake Loyd in May 2026.
Squares in an octagon	30	s = 2(11–√2)/7 = 2.73879+	3.072361017	−3.34e-01	-12.179	behind	Found by Maurizio Morandi in May 2026.
Squares in an octagon	31	s = 2.78401+	3.145317599	−3.61e-01	-12.978	behind	Found by Aapo Lipponen in July 2026.
Squares in an octagon	32	s = 2.83980+	3.187687965	−3.48e-01	-12.250	behind	Found by Aristotle Papowitz in July 2026.
Squares in an octagon	33	s = 2.85903+	3.297088467	−4.38e-01	-15.322	behind	Found by Aristotle Papowitz in July 2026.
Squares in an octagon	34	s = 7√2–7 = 2.89949+	3.353302128	−4.54e-01	-15.651	behind	Found by Mohamed Metwalli in June 2026.
Squares in an octagon	35	s = 2.90678+	3.203998337	−2.97e-01	-10.225	behind	Found by Aapo Lipponen in July 2026.
Squares in an octagon	36	s = 2.92870+	3.305943074	−3.77e-01	-12.881	behind	Found by Aristotle Papowitz in July 2026.
Squares in an octagon	37	s = 10–5√2 = 2.92893+	3.347287290	−4.18e-01	-14.284	behind
Squares in an octagon	38	s = 3.02060+	3.438501355	−4.18e-01	-13.835	behind	Found by Luke Kaiser in August 2026.
Squares in an octagon	39	s = 3.08204+	3.449821588	−3.68e-01	-11.933	behind	Found by Aapo Lipponen in July 2026.
Squares in an octagon	40	s = 3.14120+	3.436976272	−2.96e-01	-9.416	behind	Found by Aapo Lipponen in July 2026.
Tans in a circle	2	r = 1/√2 = .707+	0.707106781	−2.83e-10	-0.000	reproduced
Tans in a circle	3	r = (6 + √2)/8 = .926+	0.926776710	−1.51e-08	-0.000	reproduced	Found by Serhiy Grabarchuk in April 2005.
Tans in a circle	4	r = 1	1.033857506	−3.39e-02	-3.386	behind
Tans in a circle	5	r = 1.125+	1.142414864	−1.74e-02	-1.548	behind	Found by Maurizio Morandi in July 2007.
Tans in a circle	6	r = 1.198+	1.230269759	−3.23e-02	-2.694	behind	Found by Maurizio Morandi in July 2007.
Tans in a circle	7	r = 1.26287+	1.298359208	−3.55e-02	-2.810	behind	Found by Jake Loyd in June 2026.
Tans in a circle	8	r = √(1+1/√2) = 1.306+	1.411804337	−1.05e-01	-8.058	behind	Found by Serhiy Grabarchuk in April 2005.
Tans in a circle	9	r = 1.37381+	1.455392419	−8.16e-02	-5.938	behind	Found by Thomas Greenleaf in June 2026.
Tans in a circle	10	r = 1.42230+	1.550713364	−1.28e-01	-9.029	behind	Found by Thomas Greenleaf in June 2026.
Tans in a circle	11	r = 1.480+	1.671977663	−1.92e-01	-12.971	behind	Found by David W. Cantrell in August 2007.
Tans in a circle	12	r = 1.50878+	1.676724159	−1.68e-01	-11.131	behind	Found by Jake Loyd in June 2026.
Tans in a circle	13	r = 1.55348+	1.774378824	−2.21e-01	-14.220	behind	Found by Jake Loyd in June 2026.
Tans in a circle	14	r = √10/2 = 1.581+	1.801197255	−2.20e-01	-13.919	behind	Found by Serhiy Grabarchuk in April 2005.
Tans in a circle	15	r = 1.66443+	1.855935722	−1.92e-01	-11.506	behind	Found by Jake Loyd in June 2026.
Tans in a circle	16	r = 1.73588+	1.917727821	−1.82e-01	-10.476	behind	Found by Haowei Lin in July 2026.
Tans in a circle	17	r = 1.79723+	1.957538398	−1.60e-01	-8.920	behind	Found by Haowei Lin in July 2026.
Tans in a circle	18	r = 1.83366+	2.046264501	−2.13e-01	-11.595	behind	Found by Jake Loyd in June 2026.
Tans in a circle	19	r = 1.88814+	2.071211254	−1.83e-01	-9.696	behind	Found by Jake Loyd in June 2026.
Tans in a circle	20	r = 1.93661+	2.138882008	−2.02e-01	-10.445	behind	Found by Haowei Lin in July 2026.
Tans in a domino	2	s = 2√2/3 = .94280+	0.942809054	−1.26e-08	-0.000	reproduced	Found by Maurizio Morandi in June 2026.
Tans in a domino	3	s = .99900+	0.999003011	−3.01e-06	-0.000	reproduced	Found by Maurizio Morandi in June 2026.
Tans in a domino	4	s = 1	1.000000000	−4.00e-10	-0.000	reproduced
Tans in a domino	5	s = 1.30157+	1.326203247	−2.46e-02	-1.893	behind	Found by Jonathan Viquerat in June 2026.
Tans in a domino	6	s = 4/3 = 1.33333+	1.413271690	−7.99e-02	-5.995	behind	Found by Maurizio Morandi in June 2026.
Tans in a domino	7	s = √2 = 1.41421+	1.531403011	−1.17e-01	-8.287	behind
Tans in a domino	8	s = √2 = 1.41421+	1.684838721	−2.71e-01	-19.136	behind
Tans in a domino	9	s = 1.60710+	1.754613057	−1.48e-01	-9.179	behind	Found by Maurizio Morandi in June 2026.
Tans in a domino	10	s = 1 + 1/√2 = 1.70710+	1.937566137	−2.30e-01	-13.500	behind	Found by Maurizio Morandi in June 2026.
Tans in a domino	11	s = 1.74954+	1.916394462	−1.67e-01	-9.537	behind	Found by Aapo Lipponen in July 2026.
Tans in a domino	12	s = 3(1+√2)/4 = 1.81066+	2.058727227	−2.48e-01	-13.700	behind	Found by Maurizio Morandi in June 2026.
Tans in a domino	13	s = 1/2+√2 = 1.91421+	2.211393823	−2.97e-01	-15.525	behind	Found by Maurizio Morandi in June 2026.
Tans in a domino	14	s = (7+2√2)/5 = 1.96568+	2.161536958	−1.96e-01	-9.964	behind	Found by Maurizio Morandi in June 2026.
Tans in a domino	15	s = 2	2.298750448	−2.99e-01	-14.938	behind
Tans in a domino	16	s = 2	4.849559867	−2.8496	-142.478	behind
Tans in a domino	17	s = (7+4√2)/6 = 2.10947+	6.077841164	−3.9684	-188.121	behind	Found by Maurizio Morandi in June 2026.
Tans in a domino	18	s = 2.17527+	2.554022761	−3.79e-01	-17.412	behind	Found by Maurizio Morandi in June 2026.
Tans in a hexagon	2	s = (3+√3)/6 = .78867+	0.788675139	−4.17e-09	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Tans in a hexagon	3	s = .98882+	0.988828394	−8.39e-06	-0.001	reproduced	Found by Aapo Lippoen in July 2026.
Tans in a hexagon	4	s = 1.05845+	1.060623023	−2.17e-03	-0.205	behind	Found by Jonathan Viquerat in May 2026.
Tans in a hexagon	5	s = 1.13976+	1.206521486	−6.68e-02	-5.858	behind	Found by Jonathan Viquerat in May 2026.
Tans in a hexagon	6	s = 1.20610+	1.256012795	−4.99e-02	-4.138	behind	Found by Jonathan Viquerat in May 2026.
Tans in a hexagon	7	s = 1.30322+	1.381727441	−7.85e-02	-6.024	behind	Found by Thomas Greenleaf in June 2026.
Tans in a hexagon	8	s = 1.37728+	1.513097616	−1.36e-01	-9.861	behind	Found by Thomas Greenleaf in June 2026.
Tans in a hexagon	9	s = 1.44631+	1.610422909	−1.64e-01	-11.347	behind	Found by Thomas Greenleaf in June 2026.
Tans in a hexagon	10	s = 1.51366+	1.624540883	−1.11e-01	-7.325	behind	Found by Thomas Greenleaf in June 2026.
Tans in a hexagon	11	s = 1.59198+	1.746621637	−1.55e-01	-9.714	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	12	s = 1.65076+	1.803703629	−1.53e-01	-9.265	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	13	s = 1.70429+	1.885199934	−1.81e-01	-10.615	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	14	s = 1.76680+	3.598080950	−1.8313	-103.650	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	15	s = 1.82658+	2.037201550	−2.11e-01	-11.531	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	16	s = 1.88728+	2.096870485	−2.10e-01	-11.105	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	17	s = 1.93877+	2.186522331	−2.48e-01	-12.779	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	18	s = 1.99031+	3.939418945	−1.9491	-97.930	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	19	s = 2.03182+	3.985088660	−1.9533	-96.134	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	20	s = 2.1029+	4.050150904	−1.9473	-92.598	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	21	s = 2.14048+	4.091185985	−1.9507	-91.134	behind	Found by Jake Loyd in June 2026.
Tans in a hexagon	22	s = 2.19278+	4.247337106	−2.0546	-93.696	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	2	s = .93685+	0.936859711	−9.71e-06	-0.001	reproduced	Found by Jonathan Viquerat in May 2026.
Tans in a pentagon	3	s = 1.10580+	1.105796242	+3.76e-06	0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Tans in a pentagon	4	s = 1.28055+	1.280858944	−3.09e-04	-0.024	behind	Found by Aapo Lipponen in July 2026.
Tans in a pentagon	5	s = 1.38606+	1.386065049	−5.05e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Tans in a pentagon	6	s = 1.50657+	1.551761295	−4.52e-02	-3.000	behind	Found by Jonathan Viquerat in May 2026.
Tans in a pentagon	7	s = 1.62694+	1.708148954	−8.12e-02	-4.992	behind	Found by Jonathan Viquerat in May 2026.
Tans in a pentagon	8	s = 1.71964+	1.807841636	−8.82e-02	-5.129	behind	Found by Jonathan Viquerat in May 2026.
Tans in a pentagon	9	s = 1.79909+	1.932526649	−1.33e-01	-7.417	behind	Found by Thomas Greenleaf in June 2026.
Tans in a pentagon	10	s = 1.87393+	1.988353473	−1.14e-01	-6.106	behind	Found by Thomas Greenleaf in June 2026.
Tans in a pentagon	11	s = 1.95640+	2.040666834	−8.43e-02	-4.307	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	12	s = 2.02754+	2.190923034	−1.63e-01	-8.058	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	13	s = 2.10941+	2.332965009	−2.24e-01	-10.598	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	14	s = 2.16639+	2.402835946	−2.36e-01	-10.914	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	15	s = 2.25710+	2.393924032	−1.37e-01	-6.062	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	16	s = 2.32695+	2.531892593	−2.05e-01	-8.807	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	17	s = 2.38607+	2.705703171	−3.20e-01	-13.396	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	18	s = 2.44578+	2.716765713	−2.71e-01	-11.080	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	19	s = 2.53585+	2.871643478	−3.36e-01	-13.242	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	20	s = 2.59169+	2.883200654	−2.92e-01	-11.248	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	21	s = 2.65501+	4.964136325	−2.3091	-86.972	behind	Found by Jake Loyd in June 2026.
Tans in a pentagon	22	s = 2.71124+	5.201716421	−2.4905	-91.857	behind	Found by Jake Loyd in June 2026.
Tans in a square	2	s = 1	1.000000008	−7.89e-09	-0.000	reproduced
Tans in a square	3	s = √2 = 1.414+	1.414213563	−5.66e-10	-0.000	reproduced
Tans in a square	4	s = √2 = 1.414+	1.414213563	−5.66e-10	-0.000	reproduced
Tans in a square	5	s = 1.788+	1.788569804	−5.70e-04	-0.032	reproduced	Found by Maurizio Morandi in August 2007.
Tans in a square	6	s = 1.937+	1.998974242	−6.20e-02	-3.199	behind	Found by Maurizio Morandi in February 2008.
Tans in a square	7	s = 1.999+	2.225421265	−2.26e-01	-11.327	behind	Found by Maurizio Morandi in August 2007.
Tans in a square	8	s = 2	2.326608182	−3.27e-01	-16.330	behind
Tans in a square	9	s = 3/2 + 1/√2 = 2.207+	2.414016868	−2.07e-01	-9.375	behind	Found by Erich Friedman in March 2005.
Tans in a square	10	s = 2.393+	2.601727367	−2.09e-01	-8.722	behind	Found by Maurizio Morandi in January 2008.
Tans in a square	11	s = 1 + √2 = 2.414+	2.843844950	−4.30e-01	-17.797	behind	Found by Maurizio Morandi in August 2007.
Tans in a square	12	s = 2.61115+	2.895650245	−2.85e-01	-10.896	behind	Found by Haowei Lin in July 2026.
Tans in a square	13	s = 2.688+	3.021184818	−3.33e-01	-12.395	behind	Found by Maurizio Morandi in March 2008.
Tans in a square	14	s = 2.76345+	3.145988918	−3.83e-01	-13.843	behind	Found by Haowei Lin in July 2026.
Tans in a square	15	s = 2.82735+	3.225607371	−3.98e-01	-14.086	behind	Found by Aapo Lipponen in July 2026.
Tans in a square	16	s = 2√2 = 2.828+	3.429536608	−6.01e-01	-21.256	behind
Tans in a square	17	s = 2.970+	3.455268297	−4.85e-01	-16.339	behind	Found by David W. Cantrell in August 2007.
Tans in a square	18	s = 3	3.694063887	−6.94e-01	-23.135	behind
Tans in a square	19	s = 3.201+	3.509825728	−3.09e-01	-9.648	behind	Found by Maurizio Morandi in February 2008.
Tans in a square	20	s = 3.26857+	3.812266210	−5.44e-01	-16.634	behind	Found by Aapo Lippoen in July 2026.
Tans in a square	21	s = 3.340+	4.015812228	−6.76e-01	-20.234	behind	Found by Maurizio Morandi in March 2008.
Tans in a square	22	s = 3.392+	9.097964954	−5.7060	-168.218	behind	Found by Maurizio Morandi in December 2007.
Tans in a square	23	s = 3.464+	8.614959719	−5.1510	-148.700	behind	Found by Maurizio Morandi in December 2007.
Tans in a square	24	s = 3.517+	4.447480709	−9.30e-01	-26.457	behind	Found by David W. Cantrell in August 2007.
Tans in a tan	2	s = √2 = 1.414+	1.414213579	−1.62e-08	-0.000	reproduced
Tans in a tan	3	s = (4+√2+2√(2+2√2))/5 = 1.96179+	1.961790004	−7.85e-10	-0.000	reproduced	Found by Ed Pegg in March 2005.
Tans in a tan	4	s = 2	2.121320386	−1.21e-01	-6.066	behind
Tans in a tan	5	s = 2.405+	2.414213610	−9.21e-03	-0.383	behind	Found by David W. Cantrell in May 2005.
Tans in a tan	6	s = (12 + √6 + 5√2)/8 = 2.690+	2.785472412	−9.54e-02	-3.547	behind	Found by Maurizio Morandi in October 2007.
Tans in a tan	7	s = 2.82434+	2.854060783	−2.97e-02	-1.052	behind	Found by Maurizio Morandi in August 2007.
Tans in a tan	8	s = 2√2 = 2.828+	3.121320406	−2.93e-01	-10.357	behind
Tans in a tan	9	s = 3	3.628598247	−6.29e-01	-20.953	behind
Tans in a tan	10	s = 3.30743+	3.691378169	−3.84e-01	-11.609	behind	Found by Maurizio Morandi in August 2007.
Tans in a tan	11	s = 2 + √2 = 3.414+	3.798855355	−3.85e-01	-11.267	behind	Found by Erich Friedman in March 2005.
Tans in a tan	12	s = 3.53106+	4.172590536	−6.42e-01	-18.168	behind	Found by Maurizio Morandi in August 2007.
Tans in a tan	13	s = 3 + √2/2 = 3.707+	4.288588363	−5.81e-01	-15.686	behind	Found by Erich Friedman in March 2005.
Tans in a tan	14	s = 1 + 2√2 = 3.828+	4.394288118	−5.66e-01	-14.782	behind	Found by Erich Friedman in March 2005.
Tans in a tan	15	s = 5/2 + √2 = 3.914+	4.538814055	−6.25e-01	-15.958	behind	Found by Maurizio Morandi in August 2007.
Tans in a tan	16	s = 4	18.319627326	−14.3196	-357.991	behind
Tans in a tan	17	s = 4.181+	11.706805424	−7.5258	-180.000	behind	Found by Maurizio Morandi in August 2007.
Tans in a tan	18	s = 3√2 = 4.242+	5.140292294	−8.98e-01	-21.161	behind
Tans in a tan	19	s = 4.413+	11.706805424	−7.2938	-165.280	behind	Found by David W. Cantrell in May 2005.
Tans in a tan	20	s = 4.535+	11.706805424	−7.1718	-158.143	behind	Found by Maurizio Morandi in August 2007.
Tans in a tan	21	s = (6 + 9√2)/4 = 4.681+	11.706805424	−7.0248	-150.071	behind	Found by Maurizio Morandi in October 2007.
Tans in a tan	22	s = 3 + 5√2/4 = 4.767+	11.706805424	−6.9390	-145.564	behind	Found by Maurizio Morandi in July 2009.
Tans in a tan	23	s = 4.886+	11.706805424	−6.8208	-139.599	behind	Found by Maurizio Morandi in November 2007.
Tans in a tan	24	s = 4.947+	11.706805424	−6.7598	-136.645	behind	Found by Maurizio Morandi in October 2007.
Tans in a tan	25	s = 5	6.417199483	−1.4172	-28.344	behind
Tans in a tan	26	s = 3 + 3/√2 = 5.121+	6.431488577	−1.3102	-25.584	behind	Found by Maurizio Morandi in July 2009.
Tans in a tan	27	s = 5.241+	6.624496439	−1.3835	-26.398	behind	Found by Maurizio Morandi in July 2009.
Tans in a triangle	2	s = (1+√3)/√2 = 1.93185+	1.931851653	−7.73e-10	-0.000	reproduced
Tans in a triangle	3	s = 3/√2 = 2.12132+	2.121320344	−8.49e-10	-0.000	reproduced
Tans in a triangle	4	s = 2.53732+	2.542382915	−5.06e-03	-0.200	behind	Found by Jonathan Viquerat in May 2026.
Tans in a triangle	5	s = 2.74147+	2.777939232	−3.65e-02	-1.330	behind	Found by Jonathan Viquerat in May 2026.
Tans in a triangle	6	s = 2.93781+	2.975496730	−3.77e-02	-1.283	behind	Found by Jonathan Viquerat in May 2026.
Tans in a triangle	7	s = 3.17427+	3.481029893	−3.07e-01	-9.664	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	8	s = 3.35224+	3.616703874	−2.64e-01	-7.889	behind	Found by Jonathan Viquerat in May 2026.
Tans in a triangle	9	s = 3.51439+	3.899826183	−3.85e-01	-10.967	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	10	s = 3.69367+	3.957766256	−2.64e-01	-7.150	behind	Found by Aapo Lipponen in July 2026.
Tans in a triangle	11	s = 3.82731+	4.141753756	−3.14e-01	-8.216	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	12	s = 4	4.276158388	−2.76e-01	-6.904	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	13	s = 4.14927+	4.506795923	−3.58e-01	-8.617	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	14	s = 4.29538+	4.922257561	−6.27e-01	-14.594	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	15	s = 4.41143+	8.920536492	−4.5091	-102.214	behind	Found by Haowei Lin in July 2026.
Tans in a triangle	16	s = 4.60690+	5.184949852	−5.78e-01	-12.547	behind	Found by Haowei Lin in July 2026.
Tans in a triangle	17	s = 4.72627+	5.191171338	−4.65e-01	-9.837	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	18	s = 4.84346+	5.406582515	−5.63e-01	-11.626	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	19	s = 4.96765+	5.682558493	−7.15e-01	-14.391	behind	Found by Thomas Greenleaf in June 2026.
Tans in a triangle	20	s = 5.06562+	5.818681109	−7.53e-01	-14.866	behind	Found by Thomas Greenleaf in June 2026.
Tans in a triangle	21	s = 5.23033+	5.909566677	−6.79e-01	-12.986	behind	Found by Jonathan Loyd in June 2026.
Tans in a triangle	22	s = 5.33580+	6.119854972	−7.84e-01	-14.694	behind	Found by Jonathan Loyd in June 2026.
Tans in an L	2	s = 1/√2 = .707+	0.707106789	−8.27e-09	-0.000	reproduced
Tans in an L	3	s = (1+√7) / 4 = .911+	0.911437844	−1.63e-08	-0.000	reproduced	Found by Erich Friedman in July 2011.
Tans in an L	4	s = (√6 + √2) / 4 = .965+	0.996805449	−3.09e-02	-3.200	behind	Found by Maurizio Morandi in July 2012.
Tans in an L	5	s = 1	1.000000018	−1.76e-08	-0.000	reproduced
Tans in an L	6	s = 1	1.198614759	−1.99e-01	-19.861	behind
Tans in an L	7	s = (2 + √2) / 3 = 1.138+	1.343038089	−2.05e-01	-18.011	behind	Found by David W. Cantrell in July 2012.
Tans in an L	8	s = (1 + 2√2) / 3 = 1.276+	1.381902138	−1.06e-01	-8.288	behind	Found by Maurizio Morandi in July 2012.
Tans in an L	9	s = 4/3 = 1.333+	1.465038496	−1.32e-01	-9.880	behind	Found by Maurizio Morandi in July 2012.
Tans in an L	10	s = 1.400+	1.599553450	−2.00e-01	-14.254	behind	Found by Maurizio Morandi in July 2012.
Tans in an L	11	s = √2 = 1.414+	1.627303109	−2.13e-01	-15.070	behind
Tans in an L	12	s = √2 = 1.414+	1.672745367	−2.59e-01	-18.284	behind
Tans in an L	13	s = 1.499+	1.802993000	−3.04e-01	-20.280	behind	Found by Maurizio Morandi in July 2012.
Tans in an L	14	s = 1.607+	1.823065311	−2.16e-01	-13.445	behind	Found by Maurizio Morandi in August 2012.
Tans in an L	15	s = 1.680+	1.888452586	−2.08e-01	-12.408	behind	Found by Maurizio Morandi in August 2012.
Tans in an L	16	s = 1 + 1/√2 = 1.70711+	1.950111339	−2.43e-01	-14.235	behind	Found by Edoardo Gnaldi in September 2026.
Tans in an L	17	s = (4 + √2) / 3 = 1.804+	2.167900468	−3.63e-01	-20.131	behind	Found by Maurizio Morandi in August 2012.
Tans in an octagon	2	s = 1/√(2+√2) = .54119+	0.541196111	−1.08e-08	-0.000	reproduced
Tans in an octagon	3	s = .72389+	0.723891057	−1.06e-06	-0.000	reproduced	Found by Thomas Greenleaf in June 2026.
Tans in an octagon	4	s = √(2–√2) = .76536+	0.823112557	−5.77e-02	-7.545	behind	Found by Thomas Greenleaf in June 2026.
Tans in an octagon	5	s = .88072+	0.885270201	−4.55e-03	-0.517	behind	Found by Thomas Greenleaf in June 2026.
Tans in an octagon	6	s = √(2+√2)/2 = .92387+	0.966315669	−4.24e-02	-4.593	behind	Found by Thomas Greenleaf in June 2026.
Tans in an octagon	7	s = .98623+	1.050704072	−6.45e-02	-6.537	behind	Found by Thomas Greenleaf in June 2026.
Tans in an octagon	8	s = 1	1.086166122	−8.62e-02	-8.617	behind
Tans in an octagon	9	s = 1.08295+	1.137769913	−5.48e-02	-5.062	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	10	s = 1.09348+	1.229712724	−1.36e-01	-12.459	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	11	s = 1.15384+	1.296523621	−1.43e-01	-12.366	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	12	s = 4–2√2 = 1.17157+	1.334446276	−1.63e-01	-13.902	behind	Found by Thomas Greenleaf in June 2026.
Tans in an octagon	13	s = 1.21868+	1.581047861	−3.62e-01	-29.734	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	14	s = 3(√2–1) = 1.24264+	1.416503839	−1.74e-01	-13.991	behind	Found by Maurizio Morandi in June 2026.
Tans in an octagon	15	s = 1.31145+	1.435644151	−1.24e-01	-9.470	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	16	s = 9/√2–5 = 1.36396+	2.336525188	−9.73e-01	-71.304	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	17	s = 1.39954+	1.599856697	−2.00e-01	-14.313	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	18	s = √2 = 1.41421+	1.673502858	−2.59e-01	-18.335	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	19	s = 1.48829+	2.745258259	−1.2570	-84.457	behind	Found by Jake Loyd in June 2026.
Tans in an octagon	20	s = 35/3–43/3√2 = 1.53146+	2.790787703	−1.2593	-82.231	behind	Found by Jake Loyd in June 2026.
Triangles in a circle	2	r = √3/2 = .866+	0.866025415	−1.07e-08	-0.000	reproduced
Triangles in a circle	3	r = 3√3 – 3√2 = .953+	0.953511750	−1.48e-08	-0.000	reproduced	Found by Erich Friedman in 1997.
Triangles in a circle	4	r = .980+	0.980597945	−5.98e-04	-0.061	reproduced	Found by Erich Friedman in 1997.
Triangles in a circle	5	r = 1	1.000000000	−4.00e-10	-0.000	reproduced
Triangles in a circle	6	r = 1	1.017348607	−1.73e-02	-1.735	behind
Triangles in a circle	7	r = 1.152+	1.225775626	−7.38e-02	-6.404	behind	Found by Erich Friedman in 1997.
Triangles in a circle	8	r = 1.263+	1.265692129	−2.69e-03	-0.213	behind	Found by Maurizio Morandi in April 2008.
Triangles in a circle	9	r = 1.314+	1.314752945	−7.53e-04	-0.057	reproduced	Found by David W. Cantrell in July 2002.
Triangles in a circle	10	r = 1.38468+	1.433690309	−4.90e-02	-3.539	behind	Found by Jonathan Viquerat in June 2026.
Triangles in a circle	11	r = 1.466+	1.507265911	−4.13e-02	-2.815	behind	Found by David W. Cantrell in August 2012.
Triangles in a circle	12	r = 1.507+	1.554241772	−4.72e-02	-3.135	behind	Found by David W. Cantrell in October 2005.
Triangles in a circle	13	r = √(7/3) = 1.527+	1.600536710	−7.30e-02	-4.781	behind	Found by Erich Friedman in 1997.
Triangles in a circle	14	r = 1.60448+	1.644053397	−3.96e-02	-2.466	behind	Found by Jake Loyd in June 2026.
Triangles in a circle	15	r = 1.636+	1.714288938	−7.83e-02	-4.785	behind	Found by David W. Cantrell in July 2002.
Triangles in a circle	16	r = 1.687+	1.744893291	−5.79e-02	-3.432	behind	Found by Maurizio Morandi in April 2008.
Triangles in a circle	17	r = 1.730+	1.986286410	−2.56e-01	-14.814	behind	Found by David W. Cantrell in July 2005.
Triangles in a circle	18	r = 1.80176+	1.925460214	−1.24e-01	-6.866	behind	Found by Jake Loyd in June 2026.
Triangles in a circle	19	r = √(10/3) = 1.825+	2.179658937	−3.54e-01	-19.393	behind	Found by Haym Hirsh in August 2019.
Triangles in a circle	20	r = 1.874+	1.935533241	−6.15e-02	-3.284	behind	Found by Erich Friedman in 1997.
Triangles in a circle	21	r = 1.910+	2.227362592	−3.17e-01	-16.616	behind	Found by Maurizio Morandi in May 2008.
Triangles in a circle	22	r = 1.943+	2.295705085	−3.53e-01	-18.153	behind	Found by Maurizio Morandi in June 2008.
Triangles in a circle	23	r = 1.98467+	2.193820347	−2.09e-01	-10.538	behind	Found by Jake Loyd in June 2026.
Triangles in a circle	24	r = 2	2.399895676	−4.00e-01	-19.995	behind
Triangles in a circle	25	r = 2.055+	2.326989308	−2.72e-01	-13.235	behind	Found by David W. Cantrell in July 2005.
Triangles in a circle	26	r = 2.10664+	2.385223434	−2.79e-01	-13.224	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	27	r = 2.138+	2.436945530	−2.99e-01	-13.982	behind	Found by David W. Cantrell in July 2005.
Triangles in a circle	28	r = 2.18805+	2.493222083	−3.05e-01	-13.947	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	29	r = 2.20935+	2.577960332	−3.69e-01	-16.684	behind	Found by Jake Loyd in June 2026.
Triangles in a circle	30	r = 2.25124+	2.444410744	−1.93e-01	-8.581	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	31	r = 2.272+	2.670438342	−3.98e-01	-17.537	behind	Found by Maurizio Morandi in July 2008.
Triangles in a circle	32	r = 2.31295+	2.712977139	−4.00e-01	-17.295	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	33	r = 2.34169+	2.778738897	−4.37e-01	-18.664	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	34	r = 2.37504+	2.773470135	−3.98e-01	-16.776	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	35	r = 2.39906+	2.877579430	−4.79e-01	-19.946	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	36	r = 2.43969+	2.900518151	−4.61e-01	-18.889	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	37	r = 2.46349+	2.986146013	−5.23e-01	-21.216	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	38	r = 2.49003+	2.916608519	−4.27e-01	-17.131	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	39	r = 2.51938+	3.058872525	−5.39e-01	-21.414	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	40	r = 2.55675+	3.144224974	−5.87e-01	-22.977	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	41	r = 2.58629+	3.053224307	−4.67e-01	-18.054	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	42	r = 2.61145+	3.024584267	−4.13e-01	-15.820	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	43	r = 2.63998+	3.288522489	−6.49e-01	-24.566	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	44	r = 2.66620+	3.175594473	−5.09e-01	-19.106	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	45	r = 2.69809+	3.351300660	−6.53e-01	-24.210	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	46	r = 2.72457+	3.319291704	−5.95e-01	-21.828	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	47	r = 2.75037+	3.297428390	−5.47e-01	-19.890	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	48	r = 2.77672+	3.424720505	−6.48e-01	-23.337	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	49	r = 2.80521+	3.492750964	−6.88e-01	-24.509	behind	Found by Thomas Schadt in August 2026.
Triangles in a circle	50	r = 2.82736+	3.402536286	−5.75e-01	-20.343	behind	Found by Thomas Schadt in August 2026.
Triangles in a domino	2	s = √3/2	0.866025414	−9.95e-09	-0.000	reproduced
Triangles in a domino	3	s = .96796+	0.967967141	−7.14e-06	-0.001	reproduced	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	4	s = 1.12036+	1.120369428	−9.43e-06	-0.001	reproduced	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	5	s = 1.26315+	1.263157874	−7.87e-06	-0.001	reproduced	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	6	s = 1.37629+	1.376305156	−1.52e-05	-0.001	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	7	s = 1.49076+	1.500000029	−9.24e-03	-0.620	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	8	s = 1.56293+	1.577894783	−1.50e-02	-0.957	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	9	s = 1.64882+	1.693300500	−4.45e-02	-2.698	behind	Found by Bhavithran Ananthan in July 2026.
Triangles in a domino	10	s = 1.68302+	1.719110745	−3.61e-02	-2.144	behind	Found by Aapo Lipponen in July 2026.
Triangles in a domino	11	s = 1.72971+	1.730010548	−3.01e-04	-0.017	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a domino	12	s = 1.74022+	1.745279499	−5.06e-03	-0.291	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a domino	13	s = 1.85319+	1.858381559	−5.19e-03	-0.280	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	14	s = 3(3–√3)/2 = 1.90192+	1.930064529	−2.81e-02	-1.480	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	15	s = 1.97950+	1.980796737	−1.30e-03	-0.066	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	16	s = 2	2.083241242	−8.32e-02	-4.162	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	17	s = 2.10306+	5.508105147	−3.4050	-161.909	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	18	s = 2.14913+	2.430032310	−2.81e-01	-13.071	behind	Found by Jonathan Viquerat in April 2026.
Triangles in a domino	19	s = 2.24322+	2.425396524	−1.82e-01	-8.121	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a domino	20	s = 2.29729+	5.565288843	−3.2680	-142.255	behind	Found by Aapo Lipponen in July 2026.
Triangles in a domino	21	s = 2.36328+	5.565288843	−3.2020	-135.490	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a domino	22	s = 2.42155+	5.586312260	−3.1648	-130.692	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a domino	23	s = 2.45562+	5.603926475	−3.1483	-128.208	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a domino	24	s = 2.48387+	5.618898557	−3.1350	-126.215	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a domino	25	s = 2.52126+	5.631781512	−3.1105	-123.372	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a hexagon	2	s = √3/2 = .866+	0.866025415	−1.14e-08	-0.000	reproduced
Triangles in a hexagon	3	s = √((6+√33)/12) = .989+	0.989299542	−1.53e-08	-0.000	reproduced	Found by Erich Friedman in April 2005.
Triangles in a hexagon	4	s = 1	1.000000000	−4.00e-10	-0.000	reproduced
Triangles in a hexagon	5	s = 1	1.000000000	−4.00e-10	-0.000	reproduced
Triangles in a hexagon	6	s = 1	1.000000000	−4.00e-10	-0.000	reproduced
Triangles in a hexagon	7	s = 1.277+	1.323873213	−4.69e-02	-3.671	behind	Found by David W. Cantrell in May 2005.
Triangles in a hexagon	8	s = 1.356+	1.404491501	−4.85e-02	-3.576	behind	Found by David W. Cantrell in July 2012.
Triangles in a hexagon	9	s = 1.434+	1.435740604	−1.74e-03	-0.121	behind	Found by Erich Friedman in April 2005.
Triangles in a hexagon	10	s = 1.497+	1.497049622	−4.96e-05	-0.003	reproduced	Found by Timo Berthold et al in January 2026.
Triangles in a hexagon	11	s = 3/2 = 1.500	1.538675427	−3.87e-02	-2.578	behind	Found by Erich Friedman in April 2005.
Triangles in a hexagon	12	s = 1.623+	1.666670043	−4.37e-02	-2.691	behind	Found by Timo Berthold et al in January 2026.
Triangles in a hexagon	13	s = √(587+51√17)/12√2 = 1.663829+	1.712067735	−4.82e-02	-2.899	behind	Found by Ian Watson in April 2026.
Triangles in a hexagon	14	s = 1.725+	1.748743779	−2.37e-02	-1.376	behind	Found by David W. Cantrell in August 2012.
Triangles in a hexagon	15	s = 7/4 = 1.750	1.833334057	−8.33e-02	-4.762	behind	Found by Erich Friedman in April 2005.
Triangles in a hexagon	16	s = 9/5 = 1.800	1.997623329	−1.98e-01	-10.979	behind	Found by Maurizio Morandi in April 2008.
Triangles in a hexagon	17	s = 11/6 = 1.833+	1.939295054	−1.06e-01	-5.781	behind	Found by Maurizio Morandi in April 2008.
Triangles in a hexagon	18	s = 17/9 = 1.888+	3.321033838	−1.4321	-75.855	behind	Found by Maurizio Morandi in April 2008.
Triangles in a hexagon	19	s = 1.953+	3.324425402	−1.3714	-70.221	behind	Found by Alex Adrián Nieto in April 2026.
Triangles in a hexagon	20	s = 1.97591+	3.327120703	−1.3512	-68.384	behind	Found by Aaden Abraham in April 2026.
Triangles in a hexagon	21	s = 1.99869+	2.351315480	−3.53e-01	-17.643	behind	Found by Haowei Lin in July 2026.
Triangles in a hexagon	22	s = 2	2.388063487	−3.88e-01	-19.403	behind
Triangles in a hexagon	23	s = 2	2.456552686	−4.57e-01	-22.828	behind
Triangles in a hexagon	24	s = 2	2.472111502	−4.72e-01	-23.606	behind
Triangles in a hexagon	25	s = 13/6 = 2.16666+	2.503171561	−3.37e-01	-15.531	behind	Found by Ignacio Vallejo in April 2026.
Triangles in a hexagon	26	s = 2.21991+	2.585656334	−3.66e-01	-16.476	behind	Found by Ian Watson in April 2026.
Triangles in a hexagon	27	s = 2.29540+	2.732289525	−4.37e-01	-19.033	behind	Found by Haowei Lin in July 2026.
Triangles in a hexagon	28	s = 2.32251+	2.701008936	−3.78e-01	-16.297	behind	Found by Jake Loyd in June 2026.
Triangles in a hexagon	29	s = 7/3 = 2.33333+	2.817085329	−4.84e-01	-20.732	behind	Found by Ignacio Vallejo in April 2026.
Triangles in a hexagon	30	s = 19/8 = 2.375	3.005835889	−6.31e-01	-26.562	behind	Found by Ignacio Vallejo in April 2026.
Triangles in a hexagon	31	s = 12/5 = 2.4	2.931008618	−5.31e-01	-22.125	behind	Found by Emerson Connelly in April 2026.
Triangles in a hexagon	32	s = 2.46104+	2.882742015	−4.22e-01	-17.135	behind	Found by Haowei Lin in July 2026.
Triangles in a hexagon	33	s = 2.49038+	3.059281496	−5.69e-01	-22.844	behind	Found by Jake Loyd in June 2026.
Triangles in a hexagon	34	s = 5/2 = 2.5	3.017719064	−5.18e-01	-20.709	behind	Found by Emerson Connelly in April 2026.
Triangles in a hexagon	35	s = 5/2 = 2.5	3.020926570	−5.21e-01	-20.837	behind	Found by Emerson Connelly in April 2026.
Triangles in a hexagon	36	s = 2.58307+	3.079920255	−4.97e-01	-19.235	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a hexagon	37	s = 2.61436+	3.231197963	−6.17e-01	-23.594	behind	Found by Jake Loyd in June 2026.
Triangles in a hexagon	38	s = 2.65998+	3.307260703	−6.47e-01	-24.334	behind	Found by Jake Loyd in June 2026.
Triangles in a hexagon	39	s = 8/3 = 2.66666+	3.355894374	−6.89e-01	-25.846	behind	Found by Emerson Connelly in April 2026.
Triangles in a hexagon	40	s = 2.71131+	3.467421965	−7.56e-01	-27.887	behind	Found by Jake Loyd in June 2026.
Triangles in a hexagon	41	s = 2.73692+	3.375416520	−6.38e-01	-23.329	behind	Found by Jake Loyd in June 2026.
Triangles in a hexagon	42	s = 11/4 = 2.75	3.375782954	−6.26e-01	-22.756	behind	Found by Maurizio Morandi in May 2026.
Triangles in a hexagon	43	s = 14/5 =2.8	3.488113789	−6.88e-01	-24.575	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a hexagon	44	s = 17/6 = 2.833+	3.526700321	−6.93e-01	-24.475	behind	Found by Emerson Connelly in May 2026.
Triangles in a hexagon	45	s = 17/6 = 2.833+	3.506530888	−6.73e-01	-23.763	behind	Found by Emerson Connelly in May 2026.
Triangles in a hexagon	46	s = 2.88830+	3.680354605	−7.92e-01	-27.423	behind	Found by Jake Loyd in June 2026.
Triangles in a hexagon	47	s = 35/12 = 2.917+	3.654937694	−7.38e-01	-25.309	behind	Found by Emerson Connelly in May 2026.
Triangles in a hexagon	48	s = 47/16 =2.9375	3.683481431	−7.46e-01	-25.395	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a hexagon	49	s = 2.97693+	3.765861190	−7.89e-01	-26.502	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a hexagon	50	s = 3	3.839975639	−8.40e-01	-27.999	behind
Triangles in a hexagon	51	s = 3	3.897959190	−8.98e-01	-29.932	behind
Triangles in a hexagon	52	s = 3	3.887983218	−8.88e-01	-29.599	behind
Triangles in a hexagon	53	s = 3	3.997859456	−9.98e-01	-33.262	behind
Triangles in a hexagon	54	s = 3	4.014927454	−1.0149	-33.831	behind
Triangles in a pentagon	2	s = √(6/(3+√5)) s = 1.070+	1.070466285	−1.53e-08	-0.000	reproduced
Triangles in a pentagon	3	s = 1.143+	1.143516936	−5.17e-04	-0.045	reproduced	Found by Maurizio Morandi in August 2012.
Triangles in a pentagon	4	s = 1.199+	1.199266484	−2.66e-04	-0.022	reproduced	Found by Maurizio Morandi in July 2012.
Triangles in a pentagon	5	s = 1 + 2sin(12°)/√3 s = 1.240+	1.240075764	−7.58e-05	-0.006	reproduced	Found by Erich Friedman in March 2012.
Triangles in a pentagon	6	s = 1.393+	1.393620793	−6.21e-04	-0.045	reproduced	Found by Dominik Kamp in April 2026.
Triangles in a pentagon	7	s = 1.581+	1.633913313	−5.29e-02	-3.347	behind	Found by David W. Cantrell in July 2012.
Triangles in a pentagon	8	s = 1.659+	1.659337866	−3.38e-04	-0.020	reproduced	Found by Maurizio Morandi in July 2012.
Triangles in a pentagon	9	s = 1.767+	1.769616105	−2.62e-03	-0.148	behind	Found by Maurizio Morandi in July 2012. Improved slightly by David W. Cantrell in August 2012.
Triangles in a pentagon	10	s = 1.815+	1.856735755	−4.17e-02	-2.299	behind	Found by Timo Berthold et al in January 2026.
Triangles in a pentagon	11	s = 1.871+	1.943481247	−7.25e-02	-3.874	behind	Found by Timo Berthold et al in January 2026.
Triangles in a pentagon	12	s = 1.973+	2.001973465	−2.90e-02	-1.468	behind	Found by Ignacio Vallejo in March 2026.
Triangles in a pentagon	13	s = 2.017+	2.066053131	−4.91e-02	-2.432	behind	Found by Timo Berthold et al in January 2026.
Triangles in a pentagon	14	s = 2.088+	2.146272739	−5.83e-02	-2.791	behind	Found by Ignacio Vallejo in April 2026.
Triangles in a pentagon	15	s = 2.123+	2.178218507	−5.52e-02	-2.601	behind	Found by Ignacio Vallejo in March 2026.
Triangles in a pentagon	16	s = 2.17596+	4.221597132	−2.0456	-94.011	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	17	s = 2.23656+	2.467785921	−2.31e-01	-10.338	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	18	s = 2.29381+	2.530410744	−2.37e-01	-10.315	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	19	s = 2.344+	2.567622946	−2.24e-01	-9.540	behind	Found by Ignacio Vallejo in March 2026.
Triangles in a pentagon	20	s = 2.43345+	2.723806547	−2.90e-01	-11.932	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	21	s = 2.479+	2.852801819	−3.74e-01	-15.079	behind	Found by Ignacio Vallejo in March 2026.
Triangles in a pentagon	22	s = 2.56740+	2.850879555	−2.83e-01	-11.042	behind	Found by Ian Watson in April 2026.
Triangles in a pentagon	23	s = 2.61825+	3.020001163	−4.02e-01	-15.344	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	24	s = 2.66641+	5.450521031	−2.7841	-104.414	behind	Found by Ian Watson in April 2026.
Triangles in a pentagon	25	s = 2.71860+	3.195188869	−4.77e-01	-17.531	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	26	s = 2.76865+	3.230741290	−4.62e-01	-16.690	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	27	s = 2.81741+	3.366271388	−5.49e-01	-19.481	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	28	s = 2.86636+	3.370823568	−5.04e-01	-17.599	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	29	s = 2.90240+	3.659058202	−7.57e-01	-26.070	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	30	s = 2.95014+	3.473084939	−5.23e-01	-17.726	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	31	s = 2.98366+	3.711305949	−7.28e-01	-24.388	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	32	s = 3.02686+	3.720322160	−6.93e-01	-22.910	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	33	s = 3.06583+	3.893979055	−8.28e-01	-27.012	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	34	s = 3.11073+	3.721881385	−6.11e-01	-19.647	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	35	s = 3.14843+	3.731874118	−5.83e-01	-18.531	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	36	s = 3.17473+	3.970647627	−7.96e-01	-25.070	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	37	s = 3.21120+	3.954903127	−7.44e-01	-23.160	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	38	s = 3.24851+	4.085062981	−8.37e-01	-25.752	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	39	s = 3.29219+	4.177273091	−8.85e-01	-26.884	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	40	s = 3.32605+	4.246652288	−9.21e-01	-27.679	behind	Found by Jake Loyd in June 2026.
Triangles in a pentagon	41	s = 3.36740+	4.229598951	−8.62e-01	-25.604	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a pentagon	42	s = 3.42505+	4.286045442	−8.61e-01	-25.138	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	43	s = 3.46433+	4.451957065	−9.88e-01	-28.508	behind	Found by Aristotle Papowitz in July 2026.
Triangles in a pentagon	44	s = 3.51261+	4.656261359	−1.1437	-32.558	behind	Found by Emerson Connelly in May 2026.
Triangles in a pentagon	45	s = 3.51261+	4.433163194	−9.21e-01	-26.207	behind	Found by Emerson Connelly in May 2026.
Triangles in a pentagon	46	s = 3.61491+	4.690274431	−1.0754	-29.748	behind	Found by Emerson Connelly in May 2026.
Triangles in a pentagon	47	s = 3.65879+	4.563844707	−9.05e-01	-24.736	behind	Found by Aapo Lipponen in July 2026.
Triangles in a pentagon	48	s = 3.67605+	4.840826043	−1.1648	-31.686	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a pentagon	49	s = 3.72296+	4.715527218	−9.93e-01	-26.661	behind	Found by Emerson Connelly in May 2026.
Triangles in a pentagon	50	s = 3.75988+	4.876455595	−1.1166	-29.697	behind	Found by Emerson Connelly in May 2026.
Triangles in a square	2	s = √6/2 = 1.224+	1.224744897	−2.52e-08	-0.000	reproduced
Triangles in a square	3	s = √3/2+√6/4 = 1.478+	1.478397856	−1.67e-08	-0.000	reproduced	Found by Erich Friedman in 1996.
Triangles in a square	4	s = 1+1/√3 = 1.577+	1.577350270	−6.31e-10	-0.000	reproduced	Found by Erich Friedman in 1996.
Triangles in a square	5	s = 1.803+	1.836038542	−3.30e-02	-1.832	behind	Found by Erich Friedman in 1996.
Triangles in a square	6	s = 9/2–3√3/2 = 1.901+	1.919465815	−1.75e-02	-0.923	behind	Found by Erich Friedman in 1996.
Triangles in a square	7	s = 2	2.000000036	−3.58e-08	-0.000	reproduced	Found by Erich Friedman in 1996.
Triangles in a square	8	s = 3√3/2–1/2 = 2.098+	2.224624587	−1.27e-01	-6.032	behind	Found by Erich Friedman in 1996.
Triangles in a square	9	s = 2.287+	2.309524724	−2.25e-02	-0.985	behind	Found by Maurizio Morandi in July 2008.
Triangles in a square	10	s = 2.377+	2.464099438	−8.71e-02	-3.664	behind	Found by David W. Cantrell in July 2002.
Triangles in a square	11	s = 2.490+	2.504360088	−1.44e-02	-0.577	behind	Found by Maurizio Morandi in June 2008.
Triangles in a square	12	s = 2.558+	2.569612426	−1.16e-02	-0.454	behind	Found by Dominik Kamp in April 2026.
Triangles in a square	13	s = 2.595+	2.747740909	−1.53e-01	-5.886	behind	Found by David W. Cantrell in July 2002.
Triangles in a square	14	s = 2.726+	2.786066148	−6.01e-02	-2.203	behind	Found by David W. Cantrell in July 2002.
Triangles in a square	15	s = 2.82989+	3.021019537	−1.91e-01	-6.754	behind	Found by Jake Loyd in June 2026.
Triangles in a square	16	s = 2.9000+	3.034840483	−1.35e-01	-4.650	behind	Found by Ian Watson in April 2026.
Triangles in a square	17	s = 2.982+	5.557224225	−2.5752	-86.359	behind	Found by Maurizio Morandi in July 2008.
Triangles in a square	18	s = 3.051+	3.317163511	−2.66e-01	-8.724	behind	Found by Maurizio Morandi in July 2008.
Triangles in a square	19	s = 3.12929+	5.658081425	−2.5288	-80.810	behind	Found by Jake Loyd in June 2026.
Triangles in a square	20	s = 3.2305+	5.732236655	−2.5017	-77.441	behind	Found by Ian Watson in April 2026.
Triangles in a square	21	s = 3.31102+	3.831436743	−5.20e-01	-15.718	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	22	s = 3.3757+	7.835934344	−4.4602	-132.128	behind	Found by Ian Watson in April 2026.
Triangles in a square	23	s = 3.4311+	4.102720506	−6.72e-01	-19.574	behind	Found by Ian Watson in April 2026.
Triangles in a square	24	s = 3.46780+	5.767551096	−2.2998	-66.317	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	25	s = 3.537+	4.319965494	−7.83e-01	-22.136	behind	Found by David W. Cantrell in August 2012.
Triangles in a square	26	s = 3.575+	4.459509216	−8.85e-01	-24.742	behind	Found by Maurizio Morandi in September 2008.
Triangles in a square	27	s = 3.6726+	4.468539324	−7.96e-01	-21.672	behind	Found by Ian Watson in April 2026.
Triangles in a square	28	s = 3.75707+	4.787743515	−1.0307	-27.433	behind	Found by Jake Loyd in June 2026.
Triangles in a square	29	s = 3.81711+	4.673969962	−8.57e-01	-22.448	behind	Found by Jake Loyd in June 2026.
Triangles in a square	30	s = 3.86619+	4.330128521	−4.64e-01	-12.000	behind	Found by Jake Loyd in June 2026.
Triangles in a square	31	s = 3.93107+	4.820677202	−8.90e-01	-22.630	behind	Found by Jake Loyd in June 2026.
Triangles in a square	32	s = 3.97880+	4.911656558	−9.33e-01	-23.446	behind	Found by Jake Loyd in June 2026.
Triangles in a square	33	s = 4.05164+	5.074874847	−1.0232	-25.255	behind	Found by Jake Loyd in June 2026.
Triangles in a square	34	s = 4.09088+	5.270507016	−1.1796	-28.836	behind	Found by Jake Loyd in June 2026.
Triangles in a square	35	s = 4.14123+	5.132989635	−9.92e-01	-23.948	behind	Found by Jake Loyd in June 2026.
Triangles in a square	36	s = 4.20791+	5.418567832	−1.2107	-28.771	behind	Found by Jake Loyd in June 2026.
Triangles in a square	37	s = 4.26872+	5.384680584	−1.1160	-26.143	behind	Found by Thomas Schadt in July 2026.
Triangles in a square	38	s = 4.32008+	5.321671333	−1.0016	-23.185	behind	Found by Thomas Schadt in July 2026.
Triangles in a square	39	s = 4.36792+	5.758997862	−1.3911	-31.848	behind	Found by Jake Loyd in June 2026.
Triangles in a square	40	s = 4.41057+	4.500001473	−8.94e-02	-2.028	behind	Found by Thomas Schadt in July 2026.
Triangles in a square	41	s = 4.46431+	5.611737870	−1.1474	-25.702	behind	Found by Thomas Schadt in July 2026.
Triangles in a square	42	s = 4.51172+	5.594939354	−1.0832	-24.009	behind	Found by Thomas Schadt in July 2026.
Triangles in a square	43	s = 4.55033+	5.871529544	−1.3212	-29.035	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	44	s = 4.60023+	6.222917616	−1.6227	-35.274	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	45	s = 4.67745+	6.316335847	−1.6389	-35.038	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	46	s = 4.72960+	6.032947411	−1.3033	-27.557	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	47	s = 4.78204+	5.939610397	−1.1576	-24.207	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	48	s = 4.82632+	6.268622719	−1.4423	-29.884	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	49	s = 4.87132+	6.376228915	−1.5049	-30.893	behind	Found by Thomas Schadt in June 2026.
Triangles in a square	50	s = 4.92191+	5.500001801	−5.78e-01	-11.745	behind	Found by Thomas Schadt in June 2026.
Triangles in a tan	2	s = √3 = 1.73205+	1.732050808	−6.93e-10	-0.000	reproduced
Triangles in a tan	3	s = (√3+1)/√2 = 1.93185+	1.931851653	−7.73e-10	-0.000	reproduced
Triangles in a tan	4	s = (3+√3)/2 = 2.36602+	2.366025422	−1.78e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	5	s = (3√2+√6+2√3)/4 = 2.53905+	2.539058053	−4.13e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	6	s = √2+√(3/2) = 2.63895+	2.638958483	−4.88e-08	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	7	s = 2.78972+	2.789728398	−8.40e-06	-0.000	reproduced	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	8	s = 3.07313+	3.156596587	−8.35e-02	-2.716	behind	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	9	s = 3.18252+	3.267161842	−8.46e-02	-2.660	behind	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	10	s = 3.34084+	3.345955845	−5.12e-03	-0.153	behind	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	11	s = 3.46951+	3.575877904	−1.06e-01	-3.066	behind	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	12	s = 3.62487+	3.831068047	−2.06e-01	-5.688	behind	Found by Bhavithran Ananthan in July 2026.
Triangles in a tan	13	s = 3.71163+	4.009770726	−2.98e-01	-8.033	behind	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	14	s = 3.88268+	4.137265596	−2.55e-01	-6.557	behind	Found by Jonathan Viquerat in May 2026.
Triangles in a tan	15	s = 3.98382+	4.358797375	−3.75e-01	-9.413	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a tan	16	s = 4.03901+	4.548502480	−5.09e-01	-12.614	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a tan	17	s = 4.20066+	4.502155776	−3.01e-01	-7.177	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a tan	18	s = 4.27120+	4.532996198	−2.62e-01	-6.129	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a tan	19	s = 4.45701+	11.594276346	−7.1373	-160.136	behind	Found by Thomas Greenleaf in June 2026.
Triangles in a tan	20	s = 4.56124+	4.965124599	−4.04e-01	-8.855	behind	Found by Bhavithran Ananthan in July 2026.
Triangles in a tan	21	s = 4.64141+	11.594276346	−6.9529	-149.801	behind	Found by Akshaj Shandilya in July 2026.
Triangles in a tan	22	s = 4.73276+	11.594276346	−6.8615	-144.979	behind	Found by Akshaj Shandilya in July 2026.
Triangles in a tan	23	s = 4.82958+	11.594276346	−6.7647	-140.068	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a tan	24	s = 4.88409+	11.594276346	−6.7102	-137.389	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a tan	25	s = 5.02418+	5.964095049	−9.40e-01	-18.708	behind	Found by Jonathan Viquerat in September 2026.
Triangles in a tan	26	s = 5.10960+	6.204926156	−1.0953	-21.437	behind	Found by Akshaj Shandilya in July 2026.
Triangles in a tan	27	s = 5.19773+	6.105718949	−9.08e-01	-17.469	behind	Found by Akshaj Shandilya in July 2026.
Triangles in a tan	28	s = 5.32367+	6.346466734	−1.0228	-19.212	behind	Found by Akshaj Shandilya in July 2026.
Triangles in a tan	29	s = 5.39194+	6.241720954	−8.50e-01	-15.760	behind	Found by Found by Jonathan Viquerat in September 2026.
Triangles in a tan	30	s = 5.46057+	6.564026853	−1.1035	-20.208	behind	Found by Found by Jonathan Viquerat in September 2026.
Triangles in a triangle	2	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Triangles in a triangle	3	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Triangles in a triangle	4	s = 2	2.000000001	−8.00e-10	-0.000	reproduced
Triangles in a triangle	6	s = 13/8 + 3√13/8 = 2.977+	2.977081784	−5.58e-08	-0.000	reproduced	Found by Maurizio Morandi in August 2008.
Triangles in a triangle	7	s = 3	3.000000002	−1.82e-09	-0.000	reproduced
Triangles in a triangle	8	s = 3	3.000000032	−3.15e-08	-0.000	reproduced
Triangles in a triangle	9	s = 3	3.500000067	−5.00e-01	-16.667	behind
Triangles in a triangle	10	s = 7/2 = 3.5	3.500000660	−6.60e-07	-0.000	reproduced	Found by Erich Friedman in 1997.
Triangles in a triangle	11	s = 9/4 + 9√21/28 = 3.722+	3.914702802	−1.92e-01	-5.151	behind	Found by Erich Friedman in 1997.
Triangles in a triangle	12	s = 2 + 2cos(π/9) = 3.879+	4.000006947	−1.21e-01	-3.120	behind	Found by David W. Cantrell in July 2007.
Triangles in a triangle	13	s = 3.992+	4.232100206	−2.40e-01	-6.015	behind	Found by Maurizio Morandi in May 2008.
Triangles in a triangle	14	s = 4	4.000000083	−8.28e-08	-0.000	reproduced
Triangles in a triangle	15	s = 4	4.439724730	−4.40e-01	-10.993	behind
Triangles in a triangle	16	s = 4	4.960508825	−9.61e-01	-24.013	behind
Triangles in a triangle	17	s = 4.465+	5.237300934	−7.72e-01	-17.297	behind	Found by Maurizio Morandi in May 2008.
Triangles in a triangle	18	s = 9/2 = 4.5	5.146259006	−6.46e-01	-14.361	behind	Found by Erich Friedman in 1997.
Triangles in a triangle	19	s = 14/3 = 4.666+	5.344479586	−6.78e-01	-14.527	behind	Found by Maurizio Morandi in May 2008.
Triangles in a triangle	20	s = 33/8 + 9√21/56 = 4.861+	5.890718088	−1.0292	-21.173	behind	Found by Maurizio Morandi in May 2008.
Triangles in a triangle	21	s = 4.923+	5.987028590	−1.0640	-21.613	behind	Found by Maurizio Morandi in May 2008.
Triangles in a triangle	22	s = 4.996+	5.971954374	−9.76e-01	-19.535	behind	Found by Maurizio Morandi in May 2008.
Triangles in a triangle	23	s = 5	6.161126956	−1.1611	-23.223	behind
Triangles in a triangle	24	s = 5	6.095107402	−1.0951	-21.902	behind
Triangles in a triangle	25	s = 5	6.138835656	−1.1388	-22.777	behind
Triangles in a triangle	26	s = 5.406+	6.402804431	−9.97e-01	-18.439	behind	Found by Joah Frenzley in April 2026.
Triangles in a triangle	27	s = 11/2 = 5.5	6.520605448	−1.0206	-18.556	behind	Found by Erich Friedman in 1997.
Triangles in a triangle	28	s = 11/2 = 5.5	6.763575120	−1.2636	-22.974	behind	Found by Erich Friedman in 1997.
Triangles in a triangle	29	s = 17/3 = 5.666+	6.686938607	−1.0203	-18.007	behind	Found by David W. Cantrell in July 2007.
Triangles in a triangle	30	s = 23/4 = 5.75	7.001789755	−1.2518	-21.770	behind	Found by Maurizio Morandi in May 2008.
Triangles in a triangle	31	s = 5.90766+	6.920214741	−1.0126	-17.140	behind	Found by Thomas Schadt in June 2026.
Triangles in a triangle	32	s = 5.94593+	6.840027118	−8.94e-01	-15.037	behind	Found by Maurizio Morandi in May 2026.
Triangles in a triangle	33	s = 5.99759+	7.237575122	−1.2400	-20.675	behind	Found by Maurizio Morandi in June 2026.
Triangles in a triangle	34	s = 6	7.044338194	−1.0443	-17.406	behind
Triangles in a triangle	35	s = 6	7.528771004	−1.5288	-25.480	behind
Triangles in a triangle	36	s = 6	7.751902012	−1.7519	-29.198	behind
Triangles in a triangle	37	s = 19/3 = 6.333+	7.510264463	−1.1769	-18.584	behind	Found by Ian Watson in April 2026.
Triangles in a triangle	38	s = 6.42823+	7.667796095	−1.2396	-19.283	behind	Found by Thomas Schadt in June 2026.
Triangles in a triangle	39	s = 13/2 = 6.5	7.831204809	−1.3312	-20.480	behind	Found by Erich Friedman in April 2026.
Triangles in a triangle	40	s = 13/2 = 6.5	8.663842910	−2.1638	-33.290	behind	Found by Erich Friedman in April 2026.
Triangles in a triangle	41	s = 20/3 = 6.666+	7.954693359	−1.2880	-19.322	behind	Found by Emerson Connelly in May 2026.
Triangles in a triangle	42	s = 27/4 = 6.75	8.383962546	−1.6340	-24.207	behind	Found by Emerson Connelly in May 2026.
Triangles in a triangle	43	s = 34/5 = 6.8	8.539466288	−1.7395	-25.580	behind	Found by Emerson Connelly in May 2026.
Triangles in a triangle	44	s = 6.93076+	8.561796239	−1.6310	-23.533	behind	Found by Thomas Schadt in June 2026.
Triangles in a triangle	45	s = 6.95922+	8.572512842	−1.6133	-23.182	behind	Found by Maurizio Morandi in May 2026.
Triangles in a triangle	46	s = 6.99837+	8.750343205	−1.7520	-25.034	behind	Found by Maurizio Morandi in June 2026.
Triangles in a triangle	47	s = 7	8.911648720	−1.9116	-27.309	behind
Triangles in a triangle	48	s = 7	9.491514153	−2.4915	-35.593	behind
Triangles in a triangle	49	s = 7	8.868048538	−1.8680	-26.686	behind
Triangles in a triangle	50	s = 7 + √21/14 = 7.32732+	9.113951699	−1.7866	-24.383	behind	Found by Maurizio Morandi in May 2026.
Triangles in an L	2	s = √3/2 = .86602+	0.866025404	−3.46e-10	-0.000	reproduced
Triangles in an L	3	s = √3/2 = .86602+	0.866025404	−3.46e-10	-0.000	reproduced
Triangles in an L	4	s = .92423+	0.924231435	−1.44e-06	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Triangles in an L	5	s = 1	1.000000018	−1.79e-08	-0.000	reproduced	Found by Jonathan Viquerat in June 2026.
Triangles in an L	6	s = 1.12037+	1.125906074	−5.54e-03	-0.494	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	7	s = 1.17127+	1.223528564	−5.23e-02	-4.462	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	8	s = 1.27527+	1.300675275	−2.54e-02	-1.992	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	9	s = 1.32893+	1.356526926	−2.76e-02	-2.077	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	10	s = 1.39370+	1.459076257	−6.54e-02	-4.691	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	11	s = 1.46116+	1.535196140	−7.40e-02	-5.067	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	12	s = 3/2 = 1.5	1.565699723	−6.57e-02	-4.380	reproduced	Found by Jonathan Viquerat in June 2026.
Triangles in an L	13	s = 1.56571+	1.706117789	−1.40e-01	-8.968	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	14	s = 1.62225+	1.710716273	−8.85e-02	-5.453	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	15	s = 1.68012+	1.717682542	−3.76e-02	-2.236	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	16	s = 1.72307+	1.843873410	−1.21e-01	-7.011	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	17	s = 1.73204+	5.192307692	−3.4603	-199.780	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	18	s = 1.75029+	1.905281703	−1.55e-01	-8.855	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	19	s = 1.82181+	5.802323068	−3.9805	-218.492	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an L	20	s = 1.86706+	5.802323068	−3.9353	-210.773	behind	Found by Jonathan Viquerat in June 2026.
Triangles in an octagon	2	s = √3/√(4+2√2) = .66282+	0.662827157	−9.11e-09	-0.000	reproduced
Triangles in an octagon	3	s = .73651+	0.736539682	−2.97e-05	-0.004	behind	Found by Ignacio Vallejo in March 2026.
Triangles in an octagon	4	s = .77731+	0.777317157	−7.16e-06	-0.001	reproduced	Found by Timo Berthold et al in May 2026.
Triangles in an octagon	5	s = .80366+	0.803666304	−6.30e-06	-0.001	reproduced	Found by Nicolas Campailla in May 2026.
Triangles in an octagon	6	s = .81574+	0.953887319	−1.38e-01	-16.935	behind	Found by Ignacio Vallejo in March 2026.
Triangles in an octagon	7	s = .92453+	0.969933822	−4.54e-02	-4.911	behind	Found by Ignacio Vallejo in March 2026.
Triangles in an octagon	8	s = .98777+	1.009450113	−2.17e-02	-2.195	behind	Found by Timo Berthold et al in May 2026.
Triangles in an octagon	9	s = 1.00871+	1.066916270	−5.82e-02	-5.770	behind	Found by Grant Mowry in April 2026.
Triangles in an octagon	10	s = 1.07515+	1.206920567	−1.32e-01	-12.256	behind	Found by Jake Loyd in May 2026.
Triangles in an octagon	11	s = 1.14562+	1.169413330	−2.38e-02	-2.077	behind	Found by Grant Mowry in April 2026.
Triangles in an octagon	12	s = 1.19914+	1.228581163	−2.94e-02	-2.455	behind	Found by Timo Berthold et al in May 2026.
Triangles in an octagon	13	s = 1.23726+	1.284046604	−4.68e-02	-3.781	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	14	s = 1.27629+	1.316853962	−4.06e-02	-3.178	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	15	s = 1.30240+	1.383831225	−8.14e-02	-6.252	behind	Found by Timo Berthold et al in May 2026.
Triangles in an octagon	16	s = 1.34566+	1.401406331	−5.57e-02	-4.143	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	17	s = 1.38854+	1.457178457	−6.86e-02	-4.943	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	18	s = 1.41763+	2.467501906	−1.0499	-74.058	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	19	s = 1.46678+	2.473534509	−1.0068	-68.637	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	20	s = 1.49689+	1.682720397	−1.86e-01	-12.414	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	21	s = 1.52519+	1.771274187	−2.46e-01	-16.135	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	22	s = 1.55435+	1.781063839	−2.27e-01	-14.586	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	23	s = 1.58348+	1.804689130	−2.21e-01	-13.970	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	24	s = 1.60180+	2.574880264	−9.73e-01	-60.749	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	25	s = 1.63703+	2.052818888	−4.16e-01	-25.399	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	26	s = 1.67455+	1.887041251	−2.12e-01	-12.689	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	27	s = 1.70616+	1.945022387	−2.39e-01	-14.000	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	28	s = 1.73796+	2.008153646	−2.70e-01	-15.547	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	29	s = 1.75285+	2.084493872	−3.32e-01	-18.920	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	30	s = 1.77911+	2.177074093	−3.98e-01	-22.369	behind	Found by Jake Loyd in June 2026.
Triangles in an octagon	31	s = 1.80338+	2.250647829	−4.47e-01	-24.802	behind	Found by Aristotle Papowitz in July 2026.
Triangles in an octagon	32	s = 1.82994+	2.251290325	−4.21e-01	-23.025	behind	Found by Aristotle Papowitz in July 2026.
Triangles in an octagon	33	s = 1.84789+	2.216381407	−3.68e-01	-19.941	behind	Found by Aristotle Papowitz in July 2026.
Triangles in an octagon	34	s = 1.86454+	2.272028437	−4.07e-01	-21.855	behind	Found by Aristotle Papowitz in July 2026.
Triangles in an octagon	35	s = 1.89051+	2.320660477	−4.30e-01	-22.753	behind	Found by Aristotle Papowitz in July 2026.
Triangles in an octagon	36	s = 1.92667+	2.347292939	−4.21e-01	-21.832	behind	Found by Aristotle Papowitz in July 2026.
Triangles in an octagon	37	s = 1.95615+	2.412935193	−4.57e-01	-23.351	behind	Found by Aristotle Papowitz in July 2026.
No cases match this filter.

Data as of 2026-09-12 05:21 UTC. Every value is certified by an independent validator; none is a claim of optimality. Nothing has been submitted to the page.