Square, n = 36 record
A = 0.003805496899486…
full precision
Exact value of the published coordinate literals:
0.00380549689948663107362562072
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
67 triangles tied (within relative 10−9) at the minimal area, in 67 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.0576 · 0.1758 · 0.2181 |
(1,16,32) |
| 1 | 0.1128 · 0.2004 · 0.3089 |
(14,21,34) |
| 1 | 0.1685 · 0.1758 · 0.3414 |
(1,16,20) |
| 1 | 0.1448 · 0.2711 · 0.4140 |
(3,9,25) |
| 1 | 0.0674 · 0.3638 · 0.4283 |
(12,24,26) |
| 1 | 0.1430 · 0.2899 · 0.4312 |
(11,23,31) |
| 1 | 0.2155 · 0.2327 · 0.4469 |
(10,21,26) |
| 1 | 0.1307 · 0.3325 · 0.4618 |
(3,6,11) |
| 1 | 0.0851 · 0.3787 · 0.4619 |
(5,7,26) |
| 1 | 0.1284 · 0.3467 · 0.4737 |
(8,9,31) |
| 1 | 0.2352 · 0.2604 · 0.4946 |
(13,18,28) |
| 1 | 0.1994 · 0.2984 · 0.4968 |
(3,19,31) |
| 1 | 0.2327 · 0.2658 · 0.4976 |
(2,3,29) |
| 1 | 0.1958 · 0.3140 · 0.5089 |
(13,15,17) |
| 1 | 0.1307 · 0.4317 · 0.5615 |
(3,11,30) |
| 1 | 0.2791 · 0.2921 · 0.5706 |
(7,10,35) |
| 1 | 0.2206 · 0.3583 · 0.5783 |
(5,22,30) |
| 1 | 0.1448 · 0.4424 · 0.5864 |
(3,23,25) |
| 1 | 0.1685 · 0.4315 · 0.5994 |
(1,20,34) |
| 1 | 0.2239 · 0.3799 · 0.6033 |
(4,6,15) |
| 1 | 0.2315 · 0.3752 · 0.6061 |
(1,17,19) |
| 1 | 0.1764 · 0.4317 · 0.6074 |
(3,17,30) |
| 1 | 0.2415 · 0.4077 · 0.6487 |
(0,21,29) |
| 1 | 0.2618 · 0.3876 · 0.6490 |
(4,9,33) |
| 1 | 0.1334 · 0.5405 · 0.6733 |
(2,9,28) |
| 1 | 0.1673 · 0.5086 · 0.6754 |
(17,18,32) |
| 1 | 0.2212 · 0.4624 · 0.6831 |
(19,25,32) |
| 1 | 0.3447 · 0.3451 · 0.6894 |
(0,24,28) |
| 1 | 0.2907 · 0.4113 · 0.7017 |
(4,19,23) |
| 1 | 0.1539 · 0.5557 · 0.7091 |
(8,22,29) |
| 1 | 0.2224 · 0.5047 · 0.7267 |
(7,12,14) |
| 1 | 0.2584 · 0.4748 · 0.7329 |
(1,5,14) |
| 1 | 0.2921 · 0.4469 · 0.7387 |
(10,21,35) |
| 1 | 0.2312 · 0.5222 · 0.7531 |
(0,18,33) |
| 1 | 0.3548 · 0.4079 · 0.7625 |
(4,24,29) |
| 1 | 0.2345 · 0.5331 · 0.7673 |
(0,7,9) |
| 1 | 0.3848 · 0.4103 · 0.7948 |
(10,18,30) |
| 1 | 0.1922 · 0.6029 · 0.7948 |
(13,32,34) |
| 1 | 0.2752 · 0.5447 · 0.8197 |
(10,11,29) |
| 1 | 0.3432 · 0.5071 · 0.8501 |
(2,6,16) |
| 1 | 0.2625 · 0.5885 · 0.8508 |
(9,11,12) |
| 1 | 0.1448 · 0.7082 · 0.8526 |
(3,25,35) |
| 1 | 0.3967 · 0.4615 · 0.8580 |
(0,5,35) |
| 1 | 0.3367 · 0.5339 · 0.8704 |
(5,17,27) |
| 1 | 0.4183 · 0.4530 · 0.8712 |
(8,15,18) |
| 1 | 0.1761 · 0.7000 · 0.8759 |
(7,21,23) |
| 1 | 0.0943 · 0.7837 · 0.8775 |
(5,13,24) |
| 1 | 0.1700 · 0.7193 · 0.8891 |
(15,22,23) |
| 1 | 0.1199 · 0.7709 · 0.8905 |
(7,30,33) |
| 1 | 0.2313 · 0.6626 · 0.8937 |
(14,23,29) |
| 1 | 0.3317 · 0.5646 · 0.8961 |
(0,8,34) |
| 1 | 0.3020 · 0.6016 · 0.9034 |
(14,15,32) |
| 1 | 0.2206 · 0.6870 · 0.9074 |
(22,27,30) |
| 1 | 0.3666 · 0.5487 · 0.9152 |
(4,18,21) |
| 1 | 0.3206 · 0.6007 · 0.9211 |
(9,30,32) |
| 1 | 0.2921 · 0.6344 · 0.9264 |
(10,27,35) |
| 1 | 0.1241 · 0.8070 · 0.9308 |
(8,19,35) |
| 1 | 0.3765 · 0.5770 · 0.9533 |
(13,16,27) |
| 1 | 0.2017 · 0.7895 · 0.9910 |
(5,11,28) |
| 1 | 0.4418 · 0.5765 · 1.0182 |
(16,26,28) |
| 1 | 0.2235 · 0.8155 · 1.0388 |
(2,14,31) |
| 1 | 0.2444 · 0.8200 · 1.0642 |
(6,12,33) |
| 1 | 0.1945 · 0.8796 · 1.0739 |
(16,17,23) |
| 1 | 0.3876 · 0.7048 · 1.0923 |
(0,12,20) |
| 1 | 0.1281 · 1.0213 · 1.1492 |
(3,4,27) |
| 1 | 0.1780 · 1.0082 · 1.1860 |
(1,12,15) |
| 1 | 0.4027 · 0.8305 · 1.2331 |
(16,22,24) |
Provenance
- Found by Ilkyoo Choi, May 2026.
- Coordinates by an external contributor, re-verified here:
AlphaEvolve Early Access experiment, run 2026-05-13; re-polished in heilbronn-site (search/refine.py)— Coordinates generated during Ilkyoo Choi's AlphaEvolve experiment, re-polished to convergence by the site maintainer: 0.0038054969 against 0.0038051247 for the submitted coordinates (+0.0098%), 67 tied minimal triples (submitted: 21).. - Verified in exact arithmetic: all 7140 triples enumerated, 67 tied at the minimum.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
