Square, n = 31 record reconstructed coords
A = 0.005390372201973…
full precision
Exact value of the published coordinate literals:
0.005390372201973840243860184477
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
56 triangles tied (within relative 10−9) at the minimal area, in 56 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1170 · 0.1509 · 0.2539 |
(10,11,13) |
| 1 | 0.1189 · 0.1493 · 0.2542 |
(0,19,28) |
| 1 | 0.1238 · 0.1515 · 0.2626 |
(9,27,30) |
| 1 | 0.1189 · 0.2452 · 0.3584 |
(0,25,28) |
| 1 | 0.1686 · 0.2863 · 0.4523 |
(2,18,25) |
| 1 | 0.1518 · 0.3506 · 0.5002 |
(15,23,25) |
| 1 | 0.2484 · 0.3189 · 0.5660 |
(15,21,22) |
| 1 | 0.2947 · 0.3379 · 0.6317 |
(3,19,30) |
| 1 | 0.2760 · 0.3657 · 0.6408 |
(5,25,26) |
| 1 | 0.2720 · 0.3766 · 0.6477 |
(3,8,23) |
| 1 | 0.1836 · 0.4670 · 0.6495 |
(1,11,24) |
| 1 | 0.1745 · 0.4885 · 0.6620 |
(4,5,14) |
| 1 | 0.2025 · 0.4616 · 0.6632 |
(12,21,23) |
| 1 | 0.1875 · 0.4804 · 0.6669 |
(7,18,19) |
| 1 | 0.2516 · 0.4670 · 0.7179 |
(1,6,24) |
| 1 | 0.3124 · 0.4149 · 0.7266 |
(8,25,29) |
| 1 | 0.2527 · 0.4804 · 0.7324 |
(6,7,18) |
| 1 | 0.3707 · 0.3844 · 0.7545 |
(7,8,28) |
| 1 | 0.3743 · 0.3896 · 0.7634 |
(5,12,24) |
| 1 | 0.2947 · 0.4700 · 0.7642 |
(3,9,19) |
| 1 | 0.3379 · 0.4291 · 0.7665 |
(0,3,30) |
| 1 | 0.3314 · 0.4810 · 0.8119 |
(11,14,21) |
| 1 | 0.1439 · 0.6708 · 0.8139 |
(1,5,29) |
| 1 | 0.3279 · 0.4946 · 0.8221 |
(4,12,27) |
| 1 | 0.1579 · 0.6667 · 0.8239 |
(2,4,24) |
| 1 | 0.3260 · 0.4987 · 0.8243 |
(1,12,13) |
| 1 | 0.1445 · 0.6827 · 0.8265 |
(16,18,21) |
| 1 | 0.3293 · 0.5029 · 0.8318 |
(18,28,30) |
| 1 | 0.3338 · 0.5056 · 0.8390 |
(2,13,19) |
| 1 | 0.3311 · 0.5143 · 0.8450 |
(11,22,28) |
| 1 | 0.2484 · 0.5976 · 0.8455 |
(15,20,22) |
| 1 | 0.2628 · 0.5866 · 0.8489 |
(10,18,22) |
| 1 | 0.2709 · 0.5891 · 0.8596 |
(0,1,2) |
| 1 | 0.2683 · 0.5939 · 0.8617 |
(0,5,17) |
| 1 | 0.2647 · 0.6049 · 0.8691 |
(7,20,29) |
| 1 | 0.3855 · 0.4854 · 0.8706 |
(2,5,27) |
| 1 | 0.4223 · 0.4499 · 0.8718 |
(6,9,20) |
| 1 | 0.1396 · 0.7348 · 0.8738 |
(1,3,15) |
| 1 | 0.3808 · 0.5136 · 0.8941 |
(1,19,26) |
| 1 | 0.4073 · 0.4927 · 0.8997 |
(6,11,16) |
| 1 | 0.4134 · 0.5051 · 0.9183 |
(5,6,19) |
| 1 | 0.1579 · 0.7651 · 0.9225 |
(4,24,25) |
| 1 | 0.3260 · 0.5986 · 0.9243 |
(1,13,20) |
| 1 | 0.4156 · 0.5114 · 0.9267 |
(3,13,26) |
| 1 | 0.3279 · 0.5993 · 0.9269 |
(4,9,12) |
| 1 | 0.3338 · 0.6030 · 0.9365 |
(2,10,19) |
| 1 | 0.4446 · 0.5002 · 0.9444 |
(3,7,14) |
| 1 | 0.1869 · 0.7582 · 0.9447 |
(1,17,27) |
| 1 | 0.1745 · 0.7829 · 0.9570 |
(4,14,18) |
| 1 | 0.1980 · 0.7636 · 0.9612 |
(2,21,28) |
| 1 | 0.2516 · 0.7296 · 0.9809 |
(6,10,24) |
| 1 | 0.3614 · 0.6311 · 0.9922 |
(10,23,29) |
| 1 | 0.2527 · 0.7460 · 0.9984 |
(0,6,7) |
| 1 | 0.2720 · 0.7282 · 0.9999 |
(3,8,10) |
| 1 | 0.3506 · 0.6632 · 1.0136 |
(12,23,25) |
| 1 | 0.3350 · 0.8573 · 1.1922 |
(5,10,30) |
Provenance
- Found by Nathan Sudermann-Merx, August 2026.
- Coordinates reconstructed by local optimization:
heilbronn-site reconstruct/reconstruct.py— re-polished from the published record figure — the record holder's arrangement with re-derived coordinates; dual-verified (a/b agree exactly); all 31 points match the published record figure 1:1 (mean 2.0px, max 3.5px at figure scale). - Verified in exact arithmetic: all 4495 triples enumerated, 56 tied at the minimum.
- Friedman's page lists:
A = .005362+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
