Triangle, n = 24 record
A = 0.008985154072778…
full precision
Exact value of the published coordinate literals:
0.0089851540727786029840366633
Symmetry
Symmetry
3-fold dihedral symmetry (group D3, order 6). (Friedman's page says: fully symmetric.)
Minimal triangles
48 triangles tied (within relative 10−9) at the minimal area, in 8 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 6 | 0.3151 · 0.3569 · 0.6699 |
(2,7,9) (3,6,8) (4,10,18) (5,11,19) (12,14,23) (13,15,22) |
| 6 | 0.2590 · 0.4411 · 0.6980 |
(0,4,8) (1,5,9) (4,8,16) (5,9,17) (20,22,23) (21,22,23) |
| 6 | 0.2825 · 0.4545 · 0.7353 |
(0,2,10) (1,3,11) (6,12,16) (7,13,17) (14,19,20) (15,18,21) |
| 6 | 0.2825 · 0.5687 · 0.8500 |
(0,2,12) (1,3,13) (2,12,16) (3,13,17) (18,19,20) (18,19,21) |
| 6 | 0.2161 · 0.6393 · 0.8540 |
(2,14,22) (3,15,23) (4,6,13) (5,7,12) (8,10,19) (9,11,18) |
| 6 | 0.1715 · 0.7284 · 0.8985 |
(2,6,23) (3,7,22) (4,15,19) (5,14,18) (8,11,13) (9,10,12) |
| 6 | 0.4538 · 0.6084 · 1.0616 |
(0,7,19) (1,6,18) (2,11,20) (3,10,21) (12,15,17) (13,14,16) |
| 6 | 0.3197 · 0.8500 · 1.1692 |
(0,3,17) (0,12,21) (1,2,16) (1,13,20) (16,18,20) (17,19,21) |
Provenance
- Found by Nathan Sudermann-Merx, August 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims-2026-08-20/triangle-n24. - Verified in exact arithmetic: all 2024 triples enumerated, 48 tied at the minimum.
- Friedman's page lists:
A = .008957+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
