Triangle, n = 25 record reconstructed coords
A = 0.006993871914026…
full precision
Exact value of the published coordinate literals:
0.006993871914026839427821132947
Symmetry
Symmetry
3-fold dihedral symmetry (group D3, order 6). (Friedman's page says: not symmetric.)
Minimal triangles
45 triangles tied (within relative 10−9) at the minimal area, in 8 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 6 | 0.0552 · 0.2795 · 0.3069 |
(3,4,5) (3,4,24) (10,14,22) (11,15,16) (14,20,22) (15,16,21) |
| 6 | 0.2106 · 0.2663 · 0.4732 |
(2,11,19) (5,18,19) (9,10,19) (12,19,20) (13,19,21) (17,19,24) |
| 6 | 0.2268 · 0.5580 · 0.7838 |
(0,2,8) (0,6,12) (1,7,18) (1,13,23) (6,8,17) (7,9,23) |
| 6 | 0.3290 · 0.4913 · 0.8196 |
(2,5,21) (5,10,17) (9,20,24) (10,12,21) (11,13,20) (11,18,24) |
| 6 | 0.4525 · 0.4732 · 0.9252 |
(0,5,19) (1,19,20) (6,19,21) (7,11,19) (8,10,19) (19,23,24) |
| 6 | 0.4808 · 0.6292 · 1.1096 |
(2,16,24) (3,18,21) (4,17,20) (5,9,22) (10,13,15) (11,12,14) |
| 6 | 0.3069 · 0.9127 · 1.2194 |
(3,5,15) (3,10,22) (4,11,16) (4,14,24) (14,16,20) (15,21,22) |
| 3 | 0.2663 · 0.2663 · 0.5300 |
(2,9,19) (12,18,19) (13,17,19) |
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 2300 triples enumerated, 45 tied at the minimum.
- Friedman's page lists:
A = .006993+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
