Convex, n = 31 record reconstructed coords
A = 0.005214732673583…
full precision
Exact value of the published coordinate literals:
0.00521473267358314365559030769256
Symmetry
Not symmetric (group C1, order 1). (Friedman's page says: 5-fold dihedral symmetry.)
Minimal triangles
61 triangles tied (within relative 10−9) at the minimal area, in 59 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 2 | 29.4760 · 63.9638 · 93.0586 |
(5,14,19) (6,8,9) |
| 2 | 41.4456 · 164.4724 · 205.8706 |
(0,25,28) (15,26,29) |
| 1 | 29.4607 · 54.9508 · 83.9179 |
(0,3,15) |
| 1 | 29.4614 · 54.9508 · 83.9187 |
(0,4,15) |
| 1 | 29.4620 · 54.9594 · 83.9280 |
(10,12,22) |
| 1 | 29.4633 · 54.9625 · 83.9324 |
(11,13,27) |
| 1 | 29.4684 · 54.9594 · 83.9345 |
(10,12,28) |
| 1 | 29.4701 · 54.9625 · 83.9394 |
(13,27,29) |
| 1 | 29.4711 · 54.9764 · 83.9545 |
(8,24,30) |
| 1 | 29.4726 · 54.9783 · 83.9580 |
(1,5,20) |
| 1 | 29.4757 · 54.9764 · 83.9593 |
(6,8,30) |
| 1 | 29.4760 · 54.9783 · 83.9616 |
(1,5,14) |
| 1 | 27.7418 · 63.9311 · 91.2592 |
(10,25,26) |
| 1 | 27.7418 · 63.9326 · 91.2607 |
(25,26,27) |
| 1 | 27.7461 · 63.9347 · 91.2673 |
(0,7,18) |
| 1 | 27.7477 · 63.9375 · 91.2718 |
(15,16,17) |
| 1 | 27.7461 · 63.9473 · 91.2800 |
(7,18,30) |
| 1 | 27.7477 · 63.9511 · 91.2854 |
(1,16,17) |
| 1 | 27.7547 · 63.9545 · 91.2961 |
(12,19,23) |
| 1 | 27.7557 · 63.9578 · 91.3003 |
(2,9,13) |
| 1 | 27.7547 · 63.9638 · 91.3055 |
(5,19,23) |
| 1 | 27.7557 · 63.9646 · 91.3073 |
(2,8,9) |
| 1 | 29.4620 · 63.9311 · 93.0113 |
(10,22,25) |
| 1 | 29.4607 · 63.9347 · 93.0136 |
(0,3,7) |
| 1 | 29.4633 · 63.9326 · 93.0142 |
(11,26,27) |
| 1 | 29.4614 · 63.9375 · 93.0173 |
(4,15,16) |
| 1 | 29.4711 · 63.9473 · 93.0369 |
(18,24,30) |
| 1 | 29.4684 · 63.9545 · 93.0414 |
(12,23,28) |
| 1 | 29.4726 · 63.9511 · 93.0423 |
(1,17,20) |
| 1 | 29.4701 · 63.9578 · 93.0465 |
(2,13,29) |
| 1 | 49.8694 · 83.9179 · 133.6684 |
(3,6,15) |
| 1 | 49.8704 · 83.9187 · 133.6702 |
(0,4,14) |
| 1 | 49.8733 · 83.9280 · 133.6825 |
(12,22,29) |
| 1 | 49.8756 · 83.9324 · 133.6893 |
(11,13,28) |
| 1 | 49.8813 · 83.9345 · 133.6970 |
(10,20,28) |
| 1 | 49.8842 · 83.9394 · 133.7049 |
(24,27,29) |
| 1 | 49.8889 · 83.9545 · 133.7247 |
(4,8,24) |
| 1 | 49.8913 · 83.9580 · 133.7307 |
(3,5,20) |
| 1 | 49.8948 · 83.9593 · 133.7354 |
(6,11,30) |
| 1 | 49.8957 · 83.9616 · 133.7386 |
(1,14,22) |
| 1 | 49.7009 · 108.9984 · 158.6219 |
(7,8,14) |
| 1 | 49.7022 · 109.0005 · 158.6253 |
(5,6,16) |
| 1 | 49.7030 · 109.0069 · 158.6326 |
(13,20,25) |
| 1 | 49.7051 · 109.0121 · 158.6399 |
(12,24,26) |
| 1 | 49.7139 · 109.0242 · 158.6609 |
(1,23,29) |
| 1 | 49.7169 · 109.0307 · 158.6703 |
(2,28,30) |
| 1 | 49.7182 · 109.0411 · 158.6821 |
(11,15,18) |
| 1 | 49.7208 · 109.0464 · 158.6900 |
(0,17,22) |
| 1 | 49.7263 · 109.0539 · 158.7029 |
(4,9,27) |
| 1 | 49.7268 · 109.0558 · 158.7053 |
(3,10,19) |
| 1 | 96.0790 · 96.4586 · 192.5004 |
(0,13,21) |
| 1 | 41.4246 · 164.3884 · 205.7655 |
(1,2,11) |
| 1 | 41.4259 · 164.3927 · 205.7712 |
(22,23,30) |
| 1 | 41.4252 · 164.3956 · 205.7734 |
(5,9,24) |
| 1 | 41.4268 · 164.4025 · 205.7819 |
(8,19,20) |
| 1 | 41.4362 · 164.4316 · 205.8204 |
(3,16,27) |
| 1 | 41.4386 · 164.4412 · 205.8324 |
(4,7,10) |
| 1 | 41.4375 · 164.4459 · 205.8360 |
(13,14,17) |
| 1 | 41.4397 · 164.4545 · 205.8469 |
(6,12,18) |
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. - Verified in exact arithmetic: all 4495 triples enumerated, 61 tied at the minimum.
- Friedman's page lists:
A = .005214+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
