Triangle, n = 12 record reconstructed coords
A = 0.031004781743525…
full precision
Exact value of the published coordinate literals:
0.0310047817435253133477717385
Classes
Symmetry
Symmetry
3-fold dihedral symmetry (group D3, order 6). (Friedman's page says: completely symmetric.)
Minimal triangles
21 triangles tied (within relative 10−9) at the minimal area, in 4 congruence classes:
| count | side lengths | triangles (point indices) | |
|---|---|---|---|
| 6 | 0.3082 · 0.4632 · 0.7528 |
(3,6,7) (4,7,8) (5,6,8) (6,7,11) (6,8,10) (7,8,9) | |
| 6 | 0.2502 · 0.7658 · 1.0057 |
(0,3,10) (0,5,9) (1,3,10) (1,4,11) (2,4,11) (2,5,9) | |
| 6 | 0.5751 · 0.6451 · 1.2160 |
(0,4,6) (0,8,11) (1,5,7) (1,6,9) (2,3,8) (2,7,10) | |
| 3 | 0.2502 · 0.2502 · 0.3770 |
(0,3,9) (1,4,10) (2,5,11) |
Provenance
- Found by David Cantrell, July 2006.
- Coordinates reconstructed by local optimization:
heilbronn-site reconstruct/reconstruct.py— reconstructed by local optimization; matches published value 0.0310+ and symmetry (3-fold dihedral symmetry). - Verified in exact arithmetic: all 220 triples enumerated, 21 tied at the minimum.
- Friedman's page lists:
A = .0310+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
