Triangle, n = 13 record
A = 0.026556528919738…
full precision
Exact value of the published coordinate literals:
0.026556528919738264474389245471
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
20 triangles tied (within relative 10−9) at the minimal area, in 20 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.2685 · 0.3018 · 0.5343 |
(1,2,3) |
| 1 | 0.2335 · 0.3998 · 0.6066 |
(8,10,12) |
| 1 | 0.2249 · 0.4311 · 0.6314 |
(8,9,11) |
| 1 | 0.2685 · 0.4614 · 0.7133 |
(1,3,6) |
| 1 | 0.2875 · 0.4466 · 0.7184 |
(4,5,7) |
| 1 | 0.3242 · 0.4838 · 0.7965 |
(2,5,10) |
| 1 | 0.3556 · 0.4614 · 0.8061 |
(3,6,9) |
| 1 | 0.3259 · 0.5047 · 0.8199 |
(0,1,4) |
| 1 | 0.3998 · 0.5889 · 0.9826 |
(6,8,12) |
| 1 | 0.5047 · 0.5070 · 1.0062 |
(1,4,10) |
| 1 | 0.4838 · 0.5316 · 1.0100 |
(0,2,5) |
| 1 | 0.4311 · 0.6142 · 1.0401 |
(5,8,11) |
| 1 | 0.3470 · 0.7184 · 1.0599 |
(5,6,7) |
| 1 | 0.4283 · 0.6616 · 1.0853 |
(2,7,11) |
| 1 | 0.3259 · 0.7728 · 1.0935 |
(0,1,8) |
| 1 | 0.3470 · 0.8229 · 1.1656 |
(6,7,10) |
| 1 | 0.6066 · 0.6314 · 1.2350 |
(8,9,10) |
| 1 | 0.4736 · 0.7902 · 1.2607 |
(0,3,11) |
| 1 | 0.4736 · 0.8061 · 1.2768 |
(0,3,9) |
| 1 | 0.4646 · 0.8199 · 1.2815 |
(0,4,12) |
Provenance
- Found by Tej Stead, July 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims/01-record-triangle-n13. - Verified in exact arithmetic: all 286 triples enumerated, 20 tied at the minimum.
- Friedman's page lists:
A = .0265556+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
