Square, n = 18 record
A = 0.015526059940702…
full precision
Exact value of the published coordinate literals:
0.0155260599407024929428034301257
Symmetry
Symmetry
180° Rotationally symmetric (group C2, order 2).
18 points in 9 orbits (2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2) — hover a point to see its orbit.
Minimal triangles
30 triangles tied (within relative 10−9) at the minimal area, in 15 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 2 | 0.2171 · 0.2235 · 0.4143 |
(0,5,6) (1,4,7) |
| 2 | 0.1813 · 0.3336 · 0.4979 |
(6,12,17) (7,13,16) |
| 2 | 0.2171 · 0.3719 · 0.5784 |
(0,5,17) (1,4,16) |
| 2 | 0.1967 · 0.5101 · 0.6999 |
(0,8,14) (1,9,15) |
| 2 | 0.1813 · 0.5320 · 0.7061 |
(4,12,17) (5,13,16) |
| 2 | 0.4035 · 0.4143 · 0.8143 |
(2,4,7) (3,5,6) |
| 2 | 0.3368 · 0.4823 · 0.8154 |
(12,14,16) (13,15,17) |
| 2 | 0.2236 · 0.6073 · 0.8265 |
(4,9,11) (5,8,10) |
| 2 | 0.3446 · 0.4979 · 0.8392 |
(2,6,12) (3,7,13) |
| 2 | 0.2235 · 0.6359 · 0.8554 |
(0,6,13) (1,7,12) |
| 2 | 0.4189 · 0.5337 · 0.9503 |
(8,11,17) (9,10,16) |
| 2 | 0.4607 · 0.5407 · 0.9995 |
(6,15,16) (7,14,17) |
| 2 | 0.2235 · 0.7865 · 1.0073 |
(0,6,10) (1,7,11) |
| 2 | 0.3407 · 0.6999 · 1.0386 |
(4,8,14) (5,9,15) |
| 2 | 0.4727 · 0.7533 · 1.2248 |
(2,10,14) (3,11,15) |
Provenance
- Found by Fable 5.1 with Shengtong Zhang, September 2026.
- Coordinates by an external contributor, re-verified here:
Fable51 search campaign, September 2026: symmetry-reduced basin hopping (orbit parametrization, ruin-and-recreate, soft-min L-BFGS warm-up, trust-region SLP polish); tie system refined to 80 digits by damped Gauss-Newton; verified in exact rational arithmetic— C2 (180° rotational) symmetric, 30 tied minimal triangles; found by C2-restricted basin hopping. - Verified in exact arithmetic: all 816 triples enumerated, 30 tied at the minimum.
Record history
- 2026-07-07 0.014432+ — Tej Stead
- 2026-07-22 0.01447+ — William Shanley
- 2026-08-18 0.01459+ — Nathan Sudermann-Merx, current record (coordinates and figure not public)
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
