Convex, n = 21 record reconstructed coords
A = 0.012725160036190…
full precision
Exact value of the published coordinate literals:
0.0127251600361903942833005202643
Symmetry
Not symmetric (group C1, order 1). (Friedman's page says: no symmetry.)
Minimal triangles
37 triangles tied (within relative 10−9) at the minimal area, in 37 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 40.1953 · 44.5015 · 83.1973 |
(2,8,14) |
| 1 | 40.9613 · 43.7420 · 83.2067 |
(1,13,15) |
| 1 | 40.7854 · 44.5015 · 83.8213 |
(2,11,14) |
| 1 | 41.6928 · 43.7420 · 83.9793 |
(1,10,13) |
| 1 | 33.2552 · 85.0903 · 117.6859 |
(7,14,18) |
| 1 | 33.3193 · 85.1270 · 117.7889 |
(1,2,3) |
| 1 | 33.1981 · 85.5394 · 118.0825 |
(0,1,17) |
| 1 | 41.7249 · 83.3070 · 124.5265 |
(4,10,11) |
| 1 | 41.9555 · 85.0402 · 126.5112 |
(15,16,19) |
| 1 | 41.6451 · 86.3516 · 127.5199 |
(8,9,20) |
| 1 | 50.7685 · 82.1067 · 132.4799 |
(3,4,14) |
| 1 | 58.1321 · 76.5228 · 134.2897 |
(4,12,16) |
| 1 | 60.5814 · 75.2595 · 135.4879 |
(0,15,20) |
| 1 | 53.3471 · 82.5316 · 135.5130 |
(0,13,19) |
| 1 | 54.4287 · 81.7676 · 135.8354 |
(2,18,20) |
| 1 | 61.5022 · 75.1610 · 136.3171 |
(8,18,19) |
| 1 | 50.7685 · 106.1095 · 156.6197 |
(3,4,5) |
| 1 | 40.1953 · 117.7889 · 157.6920 |
(2,3,8) |
| 1 | 53.3471 · 104.9451 · 158.0461 |
(0,12,19) |
| 1 | 40.7854 · 117.6859 · 158.1841 |
(11,14,18) |
| 1 | 54.4287 · 104.1752 · 158.3613 |
(6,18,20) |
| 1 | 41.4977 · 117.6234 · 158.8399 |
(7,9,12) |
| 1 | 41.3519 · 118.0331 · 159.1041 |
(6,16,17) |
| 1 | 41.6928 · 118.0825 · 159.4977 |
(0,1,10) |
| 1 | 40.9613 · 119.3807 · 160.0634 |
(5,13,15) |
| 1 | 33.4970 · 131.5022 · 164.6984 |
(8,12,13) |
| 1 | 33.1291 · 131.9696 · 164.7957 |
(2,6,15) |
| 1 | 60.5814 · 104.9451 · 165.3194 |
(0,12,20) |
| 1 | 61.5022 · 104.1752 · 165.4721 |
(6,18,19) |
| 1 | 33.2552 · 133.1305 · 166.0890 |
(7,10,18) |
| 1 | 33.1981 · 133.2345 · 166.1356 |
(0,11,17) |
| 1 | 33.3193 · 133.1165 · 166.1396 |
(1,3,9) |
| 1 | 35.5214 · 133.8109 · 169.0609 |
(5,14,16) |
| 1 | 84.5520 · 110.4403 · 194.8728 |
(4,13,18) |
| 1 | 87.0329 · 111.0532 · 197.9724 |
(3,17,20) |
| 1 | 87.8659 · 112.7670 · 200.5235 |
(5,7,19) |
| 1 | 58.1321 · 158.0461 · 216.0686 |
(4,12,19) |
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 1330 triples enumerated, 37 tied at the minimum.
- Friedman's page lists:
A = .01272+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
