Convex, n = 11 record reconstructed coords
A =
= 0.0425531914893617021276595744680851063829787234…
Symmetry
Not symmetric (group C1, order 1). (Friedman's page says: 2-fold symmetry.)
Minimal triangles
28 triangles tied (within relative 10−9) at the minimal area, in 16 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 3 | 62.7076 · 75.3449 · 132.1072 |
(0,1,3) (2,4,5) (4,5,7) |
| 3 | 62.7076 · 75.6265 · 132.4286 |
(0,1,2) (3,4,5) (4,5,6) |
| 2 | 70.2874 · 75.3449 · 140.7285 |
(2,4,8) (4,8,10) |
| 2 | 70.5139 · 75.6265 · 141.2938 |
(3,5,8) (5,8,9) |
| 2 | 70.2874 · 84.0445 · 150.2590 |
(0,4,8) (2,6,9) |
| 2 | 70.5139 · 84.0445 · 150.5064 |
(1,5,8) (3,7,10) |
| 2 | 75.3449 · 132.1072 · 205.7330 |
(2,4,7) (2,5,7) |
| 2 | 75.6265 · 132.4286 · 206.3521 |
(3,4,6) (3,5,6) |
| 2 | 75.3449 · 140.7285 · 214.5282 |
(2,4,10) (2,8,10) |
| 2 | 75.6265 · 141.2938 · 215.3936 |
(3,5,9) (3,8,9) |
| 1 | 75.3449 · 96.2967 · 168.7305 |
(6,8,10) |
| 1 | 75.6265 · 96.4622 · 169.2023 |
(7,8,9) |
| 1 | 75.3449 · 104.6575 · 177.4661 |
(0,5,7) |
| 1 | 75.6265 · 105.0630 · 178.1834 |
(1,4,6) |
| 1 | 84.0445 · 109.5133 · 191.5570 |
(1,5,10) |
| 1 | 84.0445 · 109.7557 · 191.8065 |
(0,4,9) |
Provenance
- Found by David Cantrell, June 2007.
- Coordinates reconstructed by local optimization:
heilbronn-site reconstruct/reconstruct.py— reconstructed by local optimization; matches published value 0.0425+. - Verified in exact arithmetic: all 165 triples enumerated, 28 tied at the minimum.
- Friedman's page lists:
A = 2/47 = .0425+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
