Triangle, n = 15 record reconstructed coords
A = 0.021090769460248…
full precision
Exact value of the published coordinate literals:
0.021090769460248972694548017604
Classes
Symmetry
Symmetry
Approximately 120° Rotationally symmetric (group C3: the configuration sits within ~10⁻⁴ of exact symmetry, but the optimum is not exactly symmetric at coordinate precision).
Minimal triangles
15 triangles tied (within relative 10−9) at the minimal area, in 3 congruence classes:
| count | side lengths | triangles (point indices) | |
|---|---|---|---|
| 6 | 0.3987 · 0.6208 · 1.0160 |
(3,4,12) (3,5,14) (4,5,13) (6,7,12) (6,8,14) (7,8,13) | |
| 6 | 0.2819 · 0.7788 · 1.0568 |
(0,3,7) (0,5,6) (1,3,7) (1,4,8) (2,4,8) (2,5,6) | |
| 3 | 0.6668 · 0.6668 · 1.3320 |
(0,1,12) (0,2,14) (1,2,13) |
Provenance
- Found by David Cantrell, June 2007.
- Coordinates reconstructed by local optimization:
heilbronn-site reconstruct/reconstruct.py— reconstructed by local optimization; matches published value 0.0210+ and symmetry (120° Rotationally symmetric). - Verified in exact arithmetic: all 455 triples enumerated, 15 tied at the minimum.
- Friedman's page lists:
A = .0210+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
