Square, n = 24 record reconstructed coords
A = 0.008495013126523…
full precision
Exact value of the published coordinate literals:
0.008495013126523560135723571202
Symmetry
Symmetry
4-fold dihedral symmetry (group D4, order 8). (Friedman's page says: completely symmetric.)
Minimal triangles
56 triangles tied (within relative 10−9) at the minimal area, in 7 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 8 | 0.2238 · 0.3519 · 0.5725 |
(0,2,3) (1,2,3) (4,8,14) (5,9,15) (8,14,18) (9,15,19) (20,21,22) (20,21,23) |
| 8 | 0.2658 · 0.3174 · 0.5803 |
(2,7,11) (3,6,10) (6,10,14) (7,11,15) (8,12,16) (9,13,17) (12,16,21) (13,17,20) |
| 8 | 0.1950 · 0.5821 · 0.7755 |
(2,6,17) (3,7,16) (6,17,21) (7,16,20) (8,10,13) (9,11,12) (10,13,15) (11,12,14) |
| 8 | 0.3291 · 0.5725 · 0.9007 |
(0,3,5) (0,8,18) (1,2,4) (1,9,19) (4,14,22) (5,15,23) (18,20,23) (19,21,22) |
| 8 | 0.1950 · 0.7755 · 0.9695 |
(2,6,21) (2,17,21) (3,7,20) (3,16,20) (8,10,15) (8,13,15) (9,11,14) (9,12,14) |
| 8 | 0.3764 · 0.6007 · 0.9765 |
(0,12,20) (1,13,21) (2,10,22) (3,11,23) (4,7,9) (5,6,8) (14,16,19) (15,17,18) |
| 8 | 0.1950 · 0.9153 · 1.1096 |
(0,17,21) (1,16,20) (2,6,23) (3,7,22) (4,13,15) (5,12,14) (8,10,19) (9,11,18) |
Provenance
- Found by Marc-Emmanuel Coupvent des Graviers, July 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, 56 tied at the minimum.
- Friedman's page lists:
A = .008495+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
