Convex, n = 20 record reconstructed coords
A = 0.014464205030669…
full precision
Exact value of the published coordinate literals:
0.0144642050306690944890549121507
Symmetry
Not symmetric (group C1, order 1). (Friedman's page says: 5-fold dihedral symmetry.)
Minimal triangles
40 triangles tied (within relative 10−9) at the minimal area, in 40 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 47.3873 · 84.9937 · 131.3270 |
(4,6,9) |
| 1 | 47.3791 · 85.0264 · 131.3519 |
(0,13,18) |
| 1 | 47.4376 · 85.0270 · 131.4127 |
(2,4,10) |
| 1 | 47.4110 · 85.1327 · 131.4932 |
(1,8,11) |
| 1 | 47.4881 · 85.0985 · 131.5378 |
(0,8,19) |
| 1 | 47.4565 · 85.2242 · 131.6336 |
(2,5,7) |
| 1 | 47.5509 · 85.2251 · 131.7318 |
(1,5,13) |
| 1 | 47.5263 · 85.3229 · 131.8063 |
(9,17,19) |
| 1 | 47.5739 · 85.3018 · 131.8338 |
(6,7,11) |
| 1 | 47.5626 · 85.3468 · 131.8680 |
(10,17,18) |
| 1 | 82.1559 · 89.6112 · 171.3293 |
(7,10,14) |
| 1 | 82.1751 · 89.6048 · 171.3422 |
(1,15,19) |
| 1 | 82.2048 · 89.6969 · 171.4649 |
(6,14,17) |
| 1 | 82.2670 · 89.6761 · 171.5067 |
(0,3,5) |
| 1 | 82.2812 · 89.7907 · 171.6364 |
(13,15,17) |
| 1 | 82.3553 · 89.7660 · 171.6861 |
(4,11,12) |
| 1 | 82.4032 · 89.9147 · 171.8843 |
(3,7,8) |
| 1 | 82.4608 · 89.8955 · 171.9229 |
(4,16,18) |
| 1 | 82.4695 · 89.9661 · 172.0029 |
(1,2,12) |
| 1 | 82.4960 · 89.9573 · 172.0207 |
(0,9,16) |
| 1 | 41.7202 · 153.7810 · 195.0591 |
(5,16,17) |
| 1 | 41.7202 · 153.8344 · 195.1128 |
(11,16,17) |
| 1 | 41.7569 · 153.8492 · 195.1648 |
(7,12,19) |
| 1 | 41.7569 · 154.0219 · 195.3385 |
(7,12,18) |
| 1 | 41.7997 · 153.9823 · 195.3420 |
(1,3,10) |
| 1 | 41.7997 · 154.1878 · 195.5486 |
(1,3,9) |
| 1 | 41.8589 · 154.2117 · 195.6325 |
(0,6,15) |
| 1 | 41.8589 · 154.3715 · 195.7931 |
(0,2,15) |
| 1 | 41.8853 · 154.3470 · 195.7953 |
(4,13,14) |
| 1 | 41.8853 · 154.4206 · 195.8692 |
(4,8,14) |
| 1 | 89.6048 · 123.1218 · 212.4915 |
(11,15,19) |
| 1 | 89.6112 · 123.1555 · 212.5318 |
(5,10,14) |
| 1 | 89.6761 · 123.1887 · 212.6302 |
(3,5,18) |
| 1 | 89.6969 · 123.2977 · 212.7605 |
(6,14,19) |
| 1 | 89.7660 · 123.3006 · 212.8327 |
(9,11,12) |
| 1 | 89.7907 · 123.4304 · 212.9876 |
(10,13,15) |
| 1 | 89.8955 · 123.4840 · 213.1466 |
(2,16,18) |
| 1 | 89.9147 · 123.5848 · 213.2670 |
(3,6,8) |
| 1 | 89.9573 · 123.5866 · 213.3115 |
(8,9,16) |
| 1 | 89.9661 · 123.6331 · 213.3670 |
(2,12,13) |
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 1140 triples enumerated, 40 tied at the minimum.
- Friedman's page lists:
A = .01446+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
