Convex, n = 10 record reconstructed coords
A = 0.051993071522942…
full precision
Exact value of the published coordinate literals:
0.0519930715229428518406971234639
Symmetry
Symmetry
180° Rotationally symmetric (group C2, order 2). (Friedman's page says: 2-fold dihedral symmetry.)
Minimal triangles
16 triangles tied (within relative 10−9) at the minimal area, in 8 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 2 | 0.4299 · 0.6657 · 1.0503 |
(0,3,5) (1,2,4) |
| 2 | 0.4922 · 0.7170 · 1.1772 |
(6,7,8) (6,7,9) |
| 2 | 0.4299 · 0.7937 · 1.1908 |
(2,4,9) (3,5,8) |
| 2 | 0.4922 · 0.7473 · 1.2097 |
(2,7,8) (3,6,9) |
| 2 | 0.5732 · 0.7170 · 1.2650 |
(0,6,7) (1,6,7) |
| 2 | 0.5732 · 0.9119 · 1.4683 |
(0,4,6) (1,5,7) |
| 2 | 0.4922 · 1.1772 · 1.6559 |
(6,8,9) (7,8,9) |
| 2 | 0.5732 · 1.2650 · 1.8286 |
(0,1,6) (0,1,7) |
Provenance
- Found by David Cantrell, June 2007.
- Coordinates reconstructed by local optimization:
heilbronn-site reconstruct/reconstruct.py— reconstructed by local optimization; matches published value 0.0519+. - Verified in exact arithmetic: all 120 triples enumerated, 16 tied at the minimum.
- Friedman's page lists:
A = .0519+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
