Square, n = 32 record
A = 0.004690331538075…
full precision
Exact value of the published coordinate literals:
0.004690331538075156196376087259
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
58 triangles tied (within relative 10−9) at the minimal area, in 58 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1171 · 0.1313 · 0.2352 |
(23,28,30) |
| 1 | 0.1074 · 0.1456 · 0.2403 |
(1,3,8) |
| 1 | 0.1128 · 0.1604 · 0.2634 |
(0,4,7) |
| 1 | 0.1221 · 0.1621 · 0.2757 |
(24,27,31) |
| 1 | 0.1171 · 0.2314 · 0.3436 |
(16,23,28) |
| 1 | 0.1564 · 0.2705 · 0.4243 |
(16,20,25) |
| 1 | 0.1940 · 0.2782 · 0.4704 |
(2,6,11) |
| 1 | 0.1726 · 0.3361 · 0.5073 |
(9,13,16) |
| 1 | 0.1757 · 0.4243 · 0.5991 |
(16,25,29) |
| 1 | 0.2813 · 0.3288 · 0.6094 |
(29,30,31) |
| 1 | 0.2612 · 0.3563 · 0.6166 |
(16,18,22) |
| 1 | 0.2314 · 0.4180 · 0.6486 |
(7,16,23) |
| 1 | 0.1478 · 0.5107 · 0.6576 |
(9,22,26) |
| 1 | 0.3267 · 0.3332 · 0.6593 |
(0,1,2) |
| 1 | 0.2169 · 0.4481 · 0.6643 |
(7,12,21) |
| 1 | 0.1837 · 0.4864 · 0.6693 |
(9,20,23) |
| 1 | 0.2178 · 0.4979 · 0.7152 |
(1,6,13) |
| 1 | 0.3288 · 0.3992 · 0.7275 |
(28,29,31) |
| 1 | 0.3024 · 0.4271 · 0.7291 |
(2,14,19) |
| 1 | 0.3086 · 0.4227 · 0.7308 |
(8,15,27) |
| 1 | 0.2649 · 0.4831 · 0.7476 |
(15,17,25) |
| 1 | 0.3332 · 0.4179 · 0.7507 |
(0,2,3) |
| 1 | 0.3662 · 0.3900 · 0.7559 |
(7,9,14) |
| 1 | 0.2813 · 0.4760 · 0.7569 |
(27,29,30) |
| 1 | 0.3005 · 0.4864 · 0.7864 |
(2,9,20) |
| 1 | 0.1376 · 0.6499 · 0.7869 |
(12,13,19) |
| 1 | 0.3046 · 0.4866 · 0.7908 |
(23,25,31) |
| 1 | 0.1554 · 0.6576 · 0.8125 |
(5,9,26) |
| 1 | 0.3161 · 0.5043 · 0.8201 |
(0,6,8) |
| 1 | 0.1473 · 0.6789 · 0.8257 |
(11,14,20) |
| 1 | 0.2681 · 0.5607 · 0.8284 |
(6,19,27) |
| 1 | 0.3430 · 0.4873 · 0.8300 |
(8,19,31) |
| 1 | 0.3237 · 0.5123 · 0.8357 |
(1,15,24) |
| 1 | 0.2427 · 0.5939 · 0.8363 |
(20,21,27) |
| 1 | 0.2854 · 0.5544 · 0.8395 |
(4,12,25) |
| 1 | 0.2760 · 0.5708 · 0.8465 |
(19,22,28) |
| 1 | 0.2642 · 0.6013 · 0.8652 |
(3,9,12) |
| 1 | 0.3630 · 0.5246 · 0.8873 |
(5,18,30) |
| 1 | 0.3932 · 0.5138 · 0.9067 |
(0,10,15) |
| 1 | 0.1473 · 0.7693 · 0.9161 |
(11,14,16) |
| 1 | 0.2916 · 0.6298 · 0.9211 |
(23,26,27) |
| 1 | 0.4317 · 0.4933 · 0.9248 |
(15,22,30) |
| 1 | 0.3385 · 0.5895 · 0.9278 |
(1,11,27) |
| 1 | 0.4271 · 0.5062 · 0.9332 |
(2,14,24) |
| 1 | 0.1915 · 0.7464 · 0.9376 |
(0,5,19) |
| 1 | 0.3366 · 0.6104 · 0.9468 |
(3,5,7) |
| 1 | 0.3636 · 0.5847 · 0.9481 |
(0,12,28) |
| 1 | 0.2088 · 0.7464 · 0.9549 |
(5,19,24) |
| 1 | 0.1793 · 0.7844 · 0.9633 |
(11,25,30) |
| 1 | 0.2570 · 0.7274 · 0.9841 |
(4,21,29) |
| 1 | 0.2458 · 0.7408 · 0.9864 |
(4,14,15) |
| 1 | 0.3629 · 0.6259 · 0.9885 |
(5,17,27) |
| 1 | 0.2649 · 0.7306 · 0.9952 |
(15,17,28) |
| 1 | 0.4085 · 0.6166 · 1.0250 |
(16,22,24) |
| 1 | 0.3005 · 0.7377 · 1.0380 |
(2,9,28) |
| 1 | 0.3361 · 0.7152 · 1.0512 |
(1,13,16) |
| 1 | 0.3378 · 0.8434 · 1.1811 |
(7,13,27) |
| 1 | 0.3574 · 0.8756 · 1.2330 |
(1,10,28) |
Provenance
- Found by Nathan Sudermann-Merx, August 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims-2026-08-20/square-n32. - Verified in exact arithmetic: all 4960 triples enumerated, 58 tied at the minimum.
- Friedman's page lists:
A = .004642+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
