Convex, n = 12 record
A =
= 0.0392156862745098039215686274509803921568627451…
Classes
Symmetry
Symmetry
3-fold dihedral symmetry (group D3, order 6).
12 points in 3 orbits (6 + 3 + 3) — hover a point to see its orbit.
Minimal triangles
36 triangles tied (within relative 10−9) at the minimal area, in 3 congruence classes:
| count | side lengths | triangles (point indices) | |
|---|---|---|---|
| 18 | 0.5774 · 0.6667 · 1.2019 |
(0,1,10) (0,2,5) (0,3,7) (0,3,11) (1,3,7) (1,8,10) (2,3,11) (2,4,5) (3,4,7) (3,6,7) (3,8,11) (3,9,11) … | |
| 12 | 0.6667 · 1.2019 · 1.8559 |
(0,3,6) (0,3,9) (0,6,7) (0,9,11) (1,3,4) (1,4,7) (2,3,8) (2,8,11) (4,7,10) (4,10,11) (5,7,8) (5,8,11) | |
| 6 | 0.6667 · 0.8819 · 1.5275 |
(1,3,5) (1,9,11) (2,3,10) (2,6,7) (5,7,9) (6,10,11) |
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 220 triples enumerated, 36 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
