Convex, n = 14 record
A = 0.027835571458482…
full precision
Exact value of the published coordinate literals:
0.0278355714584821360301811623287
Symmetry
Not symmetric (group C1, order 1). (Friedman's page says: no symmetry.)
Minimal triangles
16 triangles tied (within relative 10−9) at the minimal area, in 16 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1658 · 0.2586 · 0.4019 |
(7,8,10) |
| 1 | 0.1693 · 0.2554 · 0.4026 |
(2,9,13) |
| 1 | 0.2011 · 0.2300 · 0.4110 |
(3,4,6) |
| 1 | 0.1970 · 0.2357 · 0.4128 |
(0,5,12) |
| 1 | 0.2344 · 0.3198 · 0.5453 |
(3,5,8) |
| 1 | 0.2344 · 0.3282 · 0.5541 |
(3,5,9) |
| 1 | 0.2024 · 0.3956 · 0.5903 |
(8,11,12) |
| 1 | 0.2265 · 0.3739 · 0.5932 |
(2,5,6) |
| 1 | 0.2580 · 0.3429 · 0.5941 |
(0,4,9) |
| 1 | 0.2639 · 0.3429 · 0.6002 |
(0,4,8) |
| 1 | 0.2265 · 0.3883 · 0.6080 |
(2,6,12) |
| 1 | 0.2024 · 0.4128 · 0.6080 |
(0,11,12) |
| 1 | 0.2065 · 0.4105 · 0.6100 |
(1,6,9) |
| 1 | 0.2065 · 0.4110 · 0.6105 |
(1,4,6) |
| 1 | 0.2317 · 0.3881 · 0.6133 |
(3,10,12) |
| 1 | 0.2317 · 0.3883 · 0.6134 |
(6,10,12) |
Provenance
- Found by AlphaEvolve, June 2025.
- Coordinates as published by AlphaEvolve (Google DeepMind):
google-deepmind/alphaevolve_results (arXiv:2506.13131). - Verified in exact arithmetic: all 364 triples enumerated, 16 tied at the minimum.
- Friedman's page lists:
A = .02783+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
