Square, n = 10 record
A =
the unique real root of
= 0.0465374195825417725616117681001455132887128455…
computed here from the Comellas–Yebra closed-form configuration (arXiv:2603.11107 appendix)
Classes
Symmetry
Symmetry
2-fold dihedral symmetry (group D2, order 4).
10 points in 3 orbits (4 + 4 + 2) — hover a point to see its orbit.
Minimal triangles
16 triangles tied (within relative 10−9) at the minimal area, in 4 congruence classes:
| count | side lengths | triangles (point indices) | |
|---|---|---|---|
| 4 | 0.2232 · 0.5898 · 0.7641 |
(0,1,2) (0,2,6) (3,7,9) (7,8,9) | |
| 4 | 0.3219 · 0.5215 · 0.8093 |
(1,4,5) (3,4,5) (4,5,6) (4,5,8) | |
| 4 | 0.3219 · 0.7023 · 1.0045 |
(0,5,8) (1,4,9) (2,3,4) (5,6,7) | |
| 4 | 0.3219 · 0.8093 · 1.1159 |
(1,4,8) (1,5,8) (3,4,6) (3,5,6) |
Provenance
- Found by F. Comellas and J. Yebra, December 2001.
- Coordinates exact, as published in:
arXiv:2603.11107— Comellas-Yebra closed form (appendix). - Verified in exact arithmetic: all 120 triples enumerated, 16 tied at the minimum.
Record history
- 2026-08-21 value identified as the unique real root of 3456A³ − 1764A² + 268A − 9 = 0 (this site, from the published closed-form configuration)
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
