Square, n = 22 record reconstructed coords
A = 0.009569817055321…
full precision
Exact value of the published coordinate literals:
0.00956981705532161841200245404
Symmetry
Symmetry
2-fold dihedral symmetry (group D2, order 4). (Friedman's page says: symmetric with respect to both diagonals.)
Minimal triangles
40 triangles tied (within relative 10−9) at the minimal area, in 10 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 4 | 0.1081 · 0.2878 · 0.3789 |
(1,5,6) (2,5,6) (7,8,9) (8,9,21) |
| 4 | 0.1935 · 0.3230 · 0.5107 |
(0,2,13) (1,13,15) (3,7,17) (14,17,21) |
| 4 | 0.1935 · 0.4029 · 0.5924 |
(0,4,13) (3,16,17) (12,14,17) (13,15,18) |
| 4 | 0.2005 · 0.4601 · 0.6575 |
(1,4,12) (2,16,18) (4,7,12) (16,18,21) |
| 4 | 0.2488 · 0.4850 · 0.7316 |
(0,5,14) (0,8,14) (3,6,15) (3,9,15) |
| 4 | 0.3370 · 0.4125 · 0.7477 |
(0,1,17) (2,15,17) (3,13,21) (7,13,14) |
| 4 | 0.2878 · 0.5430 · 0.8294 |
(1,5,10) (2,6,19) (7,8,11) (9,20,21) |
| 4 | 0.4657 · 0.5402 · 1.0052 |
(0,10,16) (3,4,20) (11,14,18) (12,15,19) |
| 4 | 0.4657 · 0.5593 · 1.0243 |
(0,11,16) (3,4,19) (10,14,18) (12,15,20) |
| 4 | 0.3230 · 0.7332 · 1.0555 |
(1,13,20) (2,11,13) (7,17,19) (10,17,21) |
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 1540 triples enumerated, 40 tied at the minimum.
- Friedman's page lists:
A = 0.009569+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
