Convex, n = 18 record
A =
= 0.0182388954634910572362139010433579317373186207…
root of
Classes
Symmetry
Symmetry
6-fold dihedral symmetry (group D6, order 12).
Minimal triangles
36 triangles tied (within relative 10−9) at the minimal area, in 3 congruence classes:
| count | side lengths | triangles (point indices) | |
|---|---|---|---|
| 12 | 0.1682 · 0.4337 · 0.5855 |
(0,1,4) (0,1,15) (0,3,4) (1,15,16) (3,4,7) (3,6,7) (6,7,10) (6,9,10) (9,10,13) (9,12,13) (12,13,16) (12,15,16) | |
| 12 | 0.2595 · 0.4711 · 0.7229 |
(0,5,8) (1,14,17) (2,4,17) (2,5,7) (2,5,15) (2,12,17) (3,8,11) (5,8,10) (6,11,14) (8,11,13) (9,14,17) (11,14,16) | |
| 12 | 0.4711 · 0.5455 · 1.0141 |
(0,5,6) (0,12,17) (1,5,7) (1,13,17) (2,3,15) (2,4,16) (3,8,9) (4,8,10) (6,11,12) (7,11,13) (9,14,15) (10,14,16) |
Provenance
- Found by Tej Stead, July 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims/03-exact-convex-n18. - Verified in exact arithmetic: all 816 triples enumerated, 36 tied at the minimum.
- Friedman's page lists:
A = [2 - (3/2 - √(239/3)/6)^(1/3) - (3/2 + √(239/3)/6)^(1/3)] / 18.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
