Convex, n = 8 record reconstructed coords
A = 0.080000139329466…
full precision
Exact value of the published coordinate literals:
0.0800001393294662954539520880303
Symmetry
Not symmetric (group C1, order 1). (Friedman's page says: 2-fold symmetry.)
Minimal triangles
10 triangles tied (within relative 10−9) at the minimal area, in 10 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.5300 · 0.5951 · 0.8593 |
(4,5,7) |
| 1 | 0.4045 · 0.7842 · 0.8095 |
(0,1,3) |
| 1 | 0.3682 · 0.8536 · 0.8805 |
(0,2,6) |
| 1 | 0.4045 · 1.0749 · 1.3879 |
(1,3,4) |
| 1 | 0.3682 · 1.1584 · 1.4356 |
(2,6,7) |
| 1 | 0.5300 · 1.0749 · 1.5462 |
(1,4,5) |
| 1 | 0.8095 · 0.8536 · 1.6180 |
(0,1,2) |
| 1 | 0.7842 · 0.9130 · 1.6548 |
(0,3,7) |
| 1 | 0.5951 · 1.1584 · 1.7106 |
(2,5,7) |
| 1 | 0.8805 · 1.0030 · 1.8532 |
(0,4,6) |
Provenance
- Found by David Cantrell, June 2007.
- Coordinates reconstructed by local optimization:
heilbronn-site reconstruct/reconstruct.py— reconstructed by local optimization; matches published value 0.0800+. - Verified in exact arithmetic: all 56 triples enumerated, 10 tied at the minimum.
- Friedman's page lists:
A = .0800+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
