Convex, n = 24 record reconstructed coords
A = 0.010712640652693…
full precision
Exact value of the published coordinate literals:
0.0107126406526936732673819821427
Symmetry
Not symmetric (group C1, order 1). (Friedman's page says: 3-fold dihedral symmetry.)
Minimal triangles
48 triangles tied (within relative 10−9) at the minimal area, in 48 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 41.5040 · 84.6182 · 125.6569 |
(5,6,12) |
| 1 | 41.5040 · 84.6208 · 125.6595 |
(6,12,23) |
| 1 | 41.5473 · 84.6825 · 125.7658 |
(4,9,10) |
| 1 | 41.5504 · 84.6896 · 125.7760 |
(1,17,21) |
| 1 | 41.5473 · 84.7215 · 125.8051 |
(4,8,9) |
| 1 | 41.5504 · 84.7260 · 125.8127 |
(1,11,17) |
| 1 | 52.2425 · 81.6478 · 133.5305 |
(7,15,23) |
| 1 | 52.2435 · 81.6513 · 133.5351 |
(5,13,16) |
| 1 | 52.2882 · 81.6960 · 133.6252 |
(3,8,20) |
| 1 | 52.2924 · 81.7029 · 133.6364 |
(11,14,19) |
| 1 | 52.3039 · 81.7497 · 133.6951 |
(10,18,22) |
| 1 | 52.3071 · 81.7531 · 133.7018 |
(0,2,21) |
| 1 | 64.0663 · 85.6300 · 149.4469 |
(9,17,20) |
| 1 | 64.0695 · 85.6328 · 149.4528 |
(1,4,19) |
| 1 | 64.0984 · 85.6934 · 149.5428 |
(1,6,15) |
| 1 | 64.1038 · 85.7006 · 149.5554 |
(9,12,16) |
| 1 | 64.1463 · 85.7350 · 149.6328 |
(2,12,17) |
| 1 | 64.1486 · 85.7394 · 149.6395 |
(4,6,18) |
| 1 | 52.2425 · 104.1566 · 156.1584 |
(7,13,23) |
| 1 | 52.2435 · 104.1566 · 156.1594 |
(5,7,13) |
| 1 | 52.2882 · 104.2654 · 156.3135 |
(3,8,22) |
| 1 | 52.2924 · 104.2730 · 156.3254 |
(0,11,14) |
| 1 | 52.3039 · 104.2654 · 156.3293 |
(3,10,22) |
| 1 | 52.3071 · 104.2730 · 156.3402 |
(0,14,21) |
| 1 | 43.4916 · 116.9335 · 160.1739 |
(3,17,19) |
| 1 | 43.4942 · 116.9420 · 160.1850 |
(4,14,20) |
| 1 | 43.5057 · 116.9365 · 160.1911 |
(1,2,7) |
| 1 | 43.5093 · 116.9451 · 160.2033 |
(9,13,18) |
| 1 | 43.5450 · 117.0654 · 160.3600 |
(0,12,15) |
| 1 | 43.5460 · 117.0656 · 160.3612 |
(6,16,22) |
| 1 | 33.3558 · 134.1261 · 167.2079 |
(1,3,18) |
| 1 | 33.3575 · 134.1305 · 167.2142 |
(2,9,14) |
| 1 | 33.3700 · 134.2236 · 167.3201 |
(7,16,17) |
| 1 | 33.3727 · 134.2348 · 167.3342 |
(4,13,15) |
| 1 | 33.3972 · 134.2909 · 167.4153 |
(0,6,19) |
| 1 | 33.3982 · 134.2978 · 167.4231 |
(12,20,22) |
| 1 | 85.8933 · 109.9050 · 195.6877 |
(8,14,16) |
| 1 | 85.8958 · 109.9094 · 195.6947 |
(3,11,15) |
| 1 | 85.9593 · 109.9750 · 195.8241 |
(0,18,23) |
| 1 | 85.9665 · 109.9843 · 195.8405 |
(2,5,22) |
| 1 | 85.9979 · 110.0418 · 195.9295 |
(7,20,21) |
| 1 | 86.0025 · 110.0467 · 195.9390 |
(10,13,19) |
| 1 | 59.4639 · 156.1584 · 215.5202 |
(11,13,23) |
| 1 | 59.4650 · 156.1594 · 215.5223 |
(5,7,8) |
| 1 | 59.5169 · 156.3135 · 215.7287 |
(8,21,22) |
| 1 | 59.5217 · 156.3254 · 215.7453 |
(0,10,11) |
| 1 | 59.5333 · 156.3293 · 215.7609 |
(3,10,23) |
| 1 | 59.5370 · 156.3402 · 215.7755 |
(5,14,21) |
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 2024 triples enumerated, 48 tied at the minimum.
- Friedman's page lists:
A = .01071+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
