Convex, n = 13 record
A = 0.030936889034895…
full precision
Exact value of the published coordinate literals:
0.0309368890348956196016368467380
Symmetry
Not symmetric (group C1, order 1). (Friedman's page says: no symmetry.)
Minimal triangles
15 triangles tied (within relative 10−9) at the minimal area, in 15 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.0525 · 0.0755 · 0.1207 |
(0,10,11) |
| 1 | 0.0525 · 0.0857 · 0.1325 |
(0,2,10) |
| 1 | 0.0641 · 0.0840 · 0.1438 |
(4,7,9) |
| 1 | 0.0652 · 0.0857 · 0.1468 |
(2,5,10) |
| 1 | 0.0609 · 0.0916 · 0.1486 |
(8,9,11) |
| 1 | 0.0724 · 0.0840 · 0.1528 |
(5,7,9) |
| 1 | 0.0684 · 0.1112 · 0.1772 |
(3,6,9) |
| 1 | 0.0794 · 0.1225 · 0.2002 |
(1,9,12) |
| 1 | 0.0684 · 0.1486 · 0.2154 |
(6,9,11) |
| 1 | 0.0838 · 0.1438 · 0.2265 |
(2,4,7) |
| 1 | 0.0794 · 0.1528 · 0.2311 |
(1,5,9) |
| 1 | 0.0901 · 0.1446 · 0.2336 |
(0,4,8) |
| 1 | 0.0609 · 0.1769 · 0.2365 |
(8,11,12) |
| 1 | 0.0724 · 0.1668 · 0.2381 |
(3,5,7) |
| 1 | 0.0641 · 0.1779 · 0.2408 |
(4,9,10) |
Provenance
- Found by David Cantrell, June 2007.
- Coordinates as published by AlphaEvolve (Google DeepMind):
google-deepmind/alphaevolve_results (arXiv:2506.13131). - Verified in exact arithmetic: all 286 triples enumerated, 15 tied at the minimum.
- Friedman's page lists:
A = .03093+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
