Triangle, n = 8 proven reconstructed coords
A =
the root near 0.0339 root of
= 0.0677892132541972123588108049740286304958007014…
polynomial for the unit right triangle; A is twice its root
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
11 triangles tied (within relative 10−9) at the minimal area, in 11 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.2111 · 0.6481 · 0.6542 |
(1,4,5) |
| 1 | 0.4347 · 0.5339 · 0.9223 |
(2,4,6) |
| 1 | 0.2111 · 0.7827 · 0.9198 |
(1,5,6) |
| 1 | 0.4356 · 0.6328 · 1.0346 |
(0,3,6) |
| 1 | 0.5339 · 0.5355 · 1.0369 |
(4,6,7) |
| 1 | 0.4510 · 0.6542 · 1.0749 |
(1,3,4) |
| 1 | 0.3703 · 0.9248 · 1.2733 |
(0,1,2) |
| 1 | 0.6481 · 0.6861 · 1.3182 |
(0,4,5) |
| 1 | 0.6328 · 0.7325 · 1.3504 |
(0,3,7) |
| 1 | 0.6403 · 0.7325 · 1.3581 |
(2,3,7) |
| 1 | 0.5355 · 0.9198 · 1.4421 |
(1,6,7) |
Provenance
- Found by David Cantrell, July 2006.
- Proved optimal by Nathan Sudermann-Merx, 2026.
- Coordinates reconstructed by local optimization:
heilbronn-site reconstruct/reconstruct.py— reconstructed by local optimization; matches published value 0.0677+ and symmetry (Not symmetric). - Verified in exact arithmetic: all 56 triples enumerated, 11 tied at the minimum.
- Friedman's page lists:
A = .0677+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
