Convex, n = 13 record
A = 0.030937207921620…
full precision
Exact value of the published coordinate literals:
0.0309372079216206390652445968483
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
19 triangles tied (within relative 10−9) at the minimal area, in 19 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.0525 · 0.0757 · 0.1210 |
(0,9,10) |
| 1 | 0.0629 · 0.0714 · 0.1285 |
(1,3,12) |
| 1 | 0.0525 · 0.0849 · 0.1316 |
(0,2,9) |
| 1 | 0.0641 · 0.0845 · 0.1444 |
(3,6,8) |
| 1 | 0.0644 · 0.0849 · 0.1451 |
(2,4,9) |
| 1 | 0.0601 · 0.0909 · 0.1470 |
(7,8,10) |
| 1 | 0.0723 · 0.0845 · 0.1533 |
(4,6,8) |
| 1 | 0.0673 · 0.1108 · 0.1756 |
(5,8,12) |
| 1 | 0.0796 · 0.1223 · 0.2003 |
(1,8,11) |
| 1 | 0.0897 · 0.1156 · 0.2038 |
(0,1,7) |
| 1 | 0.0673 · 0.1470 · 0.2128 |
(5,8,10) |
| 1 | 0.0795 · 0.1430 · 0.2213 |
(2,7,12) |
| 1 | 0.0761 · 0.1474 · 0.2223 |
(0,6,11) |
| 1 | 0.0838 · 0.1444 · 0.2271 |
(2,3,6) |
| 1 | 0.0796 · 0.1533 · 0.2318 |
(1,4,8) |
| 1 | 0.0897 · 0.1439 · 0.2326 |
(0,3,7) |
| 1 | 0.0601 · 0.1754 · 0.2343 |
(7,10,11) |
| 1 | 0.0723 · 0.1671 · 0.2383 |
(4,6,12) |
| 1 | 0.0641 · 0.1776 · 0.2405 |
(3,8,9) |
Provenance
- Found by David Cantrell, June 2007.
- Coordinates by an external contributor, re-verified here:
spiralulam heilbronn_square/csearch pipeline, ruin-and-recreate sweep 2026-08-25— stress-weighted ruin and recreate at fixed n. Improves the AlphaEvolve coordinates by 1.03e-5 relative, which is below the resolution of the displayed value. - Verified in exact arithmetic: all 286 triples enumerated, 19 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
