Convex, n = 19 record reconstructed coords
A = 0.015002704368931…
full precision
Exact value of the published coordinate literals:
0.0150027043689313202130455421158
Symmetry
Not symmetric (group C1, order 1). (Friedman's page says: no symmetry.)
Minimal triangles
32 triangles tied (within relative 10−9) at the minimal area, in 32 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 43.9267 · 85.5277 · 128.0419 |
(2,7,9) |
| 1 | 43.7847 · 85.7906 · 128.1640 |
(5,10,16) |
| 1 | 49.9748 · 88.6217 · 137.4868 |
(1,12,15) |
| 1 | 49.9196 · 89.0440 · 137.8611 |
(1,6,11) |
| 1 | 49.8745 · 89.1358 · 137.9084 |
(3,8,14) |
| 1 | 49.6525 · 89.3616 · 137.9099 |
(10,17,18) |
| 1 | 49.9502 · 89.2877 · 138.1415 |
(4,14,17) |
| 1 | 49.6190 · 89.7005 · 138.2214 |
(0,4,11) |
| 1 | 49.7872 · 89.7415 · 138.4367 |
(6,9,18) |
| 1 | 49.8494 · 89.6997 · 138.4580 |
(0,3,12) |
| 1 | 86.1953 · 93.3389 · 179.0696 |
(0,5,15) |
| 1 | 86.3946 · 93.8822 · 179.8180 |
(5,9,11) |
| 1 | 86.4102 · 94.1030 · 180.0562 |
(14,16,18) |
| 1 | 86.3015 · 94.2439 · 180.0885 |
(0,7,17) |
| 1 | 86.4421 · 94.4392 · 180.4270 |
(8,9,16) |
| 1 | 86.4660 · 94.4819 · 180.4941 |
(1,4,13) |
| 1 | 86.3854 · 94.6666 · 180.5989 |
(2,6,10) |
| 1 | 86.6073 · 94.6945 · 180.8506 |
(12,13,14) |
| 1 | 44.1101 · 160.7950 · 204.4427 |
(7,14,15) |
| 1 | 43.9267 · 161.3071 · 204.7718 |
(2,3,9) |
| 1 | 43.7847 · 161.4708 · 204.7925 |
(10,11,16) |
| 1 | 43.6619 · 161.6583 · 204.8565 |
(0,13,18) |
| 1 | 44.0514 · 161.6399 · 205.2326 |
(1,5,17) |
| 1 | 43.9267 · 161.8411 · 205.3085 |
(2,4,9) |
| 1 | 44.1101 · 161.9039 · 205.5573 |
(6,7,14) |
| 1 | 43.7847 · 162.3047 · 205.6306 |
(10,12,16) |
| 1 | 93.3389 · 129.1726 · 222.2623 |
(3,5,15) |
| 1 | 93.8822 · 129.3867 · 223.0224 |
(5,11,18) |
| 1 | 94.2439 · 129.1560 · 223.1540 |
(7,11,17) |
| 1 | 94.1030 · 129.6227 · 223.4808 |
(4,16,18) |
| 1 | 94.6666 · 129.3430 · 223.7659 |
(2,6,17) |
| 1 | 94.4819 · 129.7014 · 223.9399 |
(4,6,13) |
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 969 triples enumerated, 32 tied at the minimum.
- Friedman's page lists:
A = .01500+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
