Square, n = 28 record reconstructed coords
A = 0.006775810239336…
full precision
Exact value of the published coordinate literals:
0.0067758102393368038155656289525
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 | 0.1108 · 0.2171 · 0.3149 |
(4,6,24) (4,6,26) (5,7,20) (5,7,25) (16,18,22) (16,18,27) (17,19,21) (17,19,23) |
| 8 | 0.2171 · 0.3361 · 0.5508 |
(4,24,25) (5,24,25) (6,26,27) (7,20,21) (16,26,27) (17,20,21) (18,22,23) (19,22,23) |
| 8 | 0.2017 · 0.4048 · 0.6046 |
(1,3,21) (1,3,27) (1,13,23) (1,13,25) (3,12,22) (3,12,24) (12,13,20) (12,13,26) |
| 8 | 0.2744 · 0.3753 · 0.6484 |
(0,2,16) (0,2,17) (4,10,14) (5,11,15) (6,8,9) (7,8,9) (10,14,18) (11,15,19) |
| 8 | 0.1560 · 0.6904 · 0.8455 |
(0,8,22) (0,8,24) (2,9,23) (2,9,25) (10,11,20) (10,11,26) (14,15,21) (14,15,27) |
| 8 | 0.2593 · 0.6583 · 0.9170 |
(0,3,25) (1,2,24) (1,15,26) (3,14,20) (8,12,23) (9,13,22) (10,12,21) (11,13,27) |
| 8 | 0.4813 · 0.6010 · 1.0820 |
(1,7,22) (1,18,20) (3,6,23) (3,19,26) (4,13,21) (5,12,27) (12,16,25) (13,17,24) |
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 3276 triples enumerated, 56 tied at the minimum.
- Friedman's page lists:
A = .006775+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
