Convex, n = 16 record reconstructed coords
A = 0.022272877128980…
full precision
Exact value of the published coordinate literals:
0.0222728771289807384536723067288
Classes
Symmetry
Symmetry
4-fold dihedral symmetry (group D4, order 8).
Minimal triangles
28 triangles tied (within relative 10−9) at the minimal area, in 4 congruence classes:
| count | side lengths | triangles (point indices) | |
|---|---|---|---|
| 8 | 0.4979 · 0.5464 · 1.0065 |
(4,8,12) (4,11,12) (5,8,13) (5,9,13) (6,9,14) (6,10,14) (7,10,15) (7,11,15) | |
| 8 | 0.5587 · 0.6530 · 1.1884 |
(0,1,6) (0,1,15) (0,3,5) (0,3,14) (1,2,7) (1,2,12) (2,3,4) (2,3,13) | |
| 8 | 0.7864 · 1.1884 · 1.9695 |
(0,5,10) (0,9,15) (1,6,11) (1,10,12) (2,7,8) (2,11,13) (3,4,9) (3,8,14) | |
| 4 | 0.5464 · 0.5464 · 1.0604 |
(4,11,15) (5,8,12) (6,9,13) (7,10,14) |
Provenance
- Found by David Cantrell, June 2007.
- Coordinates reconstructed by local optimization:
heilbronn-site reconstruct/reconstruct.py— reconstructed by local optimization; matches published value 0.0222+ and symmetry (4-fold dihedral symmetry). - Verified in exact arithmetic: all 560 triples enumerated, 28 tied at the minimum.
- Friedman's page lists:
A = .0222+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
