Convex, n = 11 record
A =
= 0.0425531914893617021276595744680851063829787234…
Symmetry
Symmetry
Mirror symmetric (group D1, order 2).
11 points in 6 orbits (2 + 2 + 2 + 2 + 2 + 1) — hover a point to see its orbit.
Minimal triangles
28 triangles tied (within relative 10−9) at the minimal area, in 8 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 6 | 0.3333 · 0.4006 · 0.7027 |
(0,1,2) (0,1,3) (2,4,5) (3,4,5) (4,5,6) (4,5,7) |
| 4 | 0.3727 · 0.4006 · 0.7474 |
(2,4,8) (3,5,8) (4,8,10) (5,8,9) |
| 4 | 0.3727 · 0.4444 · 0.7954 |
(0,4,8) (1,5,8) (2,6,9) (3,7,10) |
| 4 | 0.4006 · 0.7027 · 1.0943 |
(2,4,7) (2,5,7) (3,4,6) (3,5,6) |
| 4 | 0.4006 · 0.7474 · 1.1399 |
(2,4,10) (2,8,10) (3,5,9) (3,8,9) |
| 2 | 0.4006 · 0.5122 · 0.8975 |
(6,8,10) (7,8,9) |
| 2 | 0.4006 · 0.5556 · 0.9428 |
(0,5,7) (1,4,6) |
| 2 | 0.4444 · 0.5800 · 1.0138 |
(0,4,9) (1,5,10) |
Provenance
- Found by David Cantrell, June 2007.
- Coordinates by an external contributor, re-verified here:
David Cantrell's Mathematica notebook UltimateHeilbronn.nb (2007), received September 2026— Original author's arrangement, previously shown only as a reconstruction; given exactly in the notebook.. - Verified in exact arithmetic: all 165 triples enumerated, 28 tied at the minimum.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
