Convex, n = 14 record
A = 0.027835580517553…
full precision
Exact value of the published coordinate literals:
0.0278355805175536958217283409308
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
21 triangles tied (within relative 10−9) at the minimal area, in 21 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1671 · 0.2489 · 0.3943 |
(5,6,8) |
| 1 | 0.1686 · 0.2479 · 0.3950 |
(7,10,11) |
| 1 | 0.1975 · 0.2251 · 0.4031 |
(1,2,4) |
| 1 | 0.1929 · 0.2316 · 0.4051 |
(0,3,9) |
| 1 | 0.2290 · 0.3118 · 0.5320 |
(1,3,6) |
| 1 | 0.2290 · 0.3213 · 0.5419 |
(1,3,7) |
| 1 | 0.1983 · 0.3864 · 0.5772 |
(6,9,13) |
| 1 | 0.2210 · 0.3647 · 0.5786 |
(3,4,11) |
| 1 | 0.2516 · 0.3350 · 0.5798 |
(0,2,7) |
| 1 | 0.2582 · 0.3350 · 0.5867 |
(0,2,6) |
| 1 | 0.2210 · 0.3794 · 0.5937 |
(4,9,11) |
| 1 | 0.1983 · 0.4051 · 0.5965 |
(0,9,13) |
| 1 | 0.2030 · 0.4031 · 0.5993 |
(2,4,12) |
| 1 | 0.2030 · 0.4032 · 0.5994 |
(4,7,12) |
| 1 | 0.2268 · 0.3794 · 0.5998 |
(4,8,9) |
| 1 | 0.2268 · 0.3808 · 0.6013 |
(1,8,9) |
| 1 | 0.1929 · 0.4704 · 0.6578 |
(0,3,12) |
| 1 | 0.2910 · 0.3720 · 0.6584 |
(5,9,12) |
| 1 | 0.1975 · 0.4900 · 0.6826 |
(1,2,13) |
| 1 | 0.3316 · 0.3949 · 0.7231 |
(0,1,11) |
| 1 | 0.3459 · 0.4134 · 0.7563 |
(2,3,8) |
Provenance
- Found by AlphaEvolve, June 2025.
- Coordinates by an external contributor, re-verified here:
spiralulam heilbronn_square/csearch pipeline, ruin-and-recreate sweep 2026-08-26— a structurally different configuration from the AlphaEvolve one, not a re-polish of it: the pairwise distance spectra differ by up to 3.3 per cent after affine normalisation, yet the values agree to seven digits. - Verified in exact arithmetic: all 364 triples enumerated, 21 tied at the minimum.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
