Convex, n = 12 record reconstructed coords
A =
= 0.0392156862745098039215686274509803921568627451…
Classes
Symmetry
Symmetry
3-fold dihedral symmetry (group D3, order 6).
Minimal triangles
36 triangles tied (within relative 10−9) at the minimal area, in 3 congruence classes:
| count | side lengths | triangles (point indices) | |
|---|---|---|---|
| 18 | 0.6951 · 0.8026 · 1.4470 |
(0,1,3) (0,1,7) (0,1,8) (0,1,9) (0,2,5) (0,2,6) (0,2,7) (0,2,11) (1,2,4) (1,2,6) (1,2,8) (1,2,10) … | |
| 12 | 0.8026 · 1.4470 · 2.2345 |
(0,3,7) (0,5,6) (0,7,11) (0,8,9) (1,3,7) (1,4,8) (1,6,10) (1,8,9) (2,4,8) (2,5,6) (2,6,10) (2,7,11) | |
| 6 | 0.8026 · 1.0618 · 1.8391 |
(0,4,5) (0,9,10) (1,3,5) (1,10,11) (2,3,4) (2,9,11) |
Provenance
- Found by David Cantrell, June 2007.
- Coordinates reconstructed by local optimization:
heilbronn-site reconstruct/reconstruct.py— reconstructed by local optimization; matches published value 0.0392+ and symmetry (3-fold dihedral symmetry). - Verified in exact arithmetic: all 220 triples enumerated, 36 tied at the minimum.
- Friedman's page lists:
A = 2/51 = .0392+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
