Triangle, n = 18 record reconstructed coords
A = 0.014894342987958…
full precision
Exact value of the published coordinate literals:
0.014894342987958971827277617711
Classes
Symmetry
Symmetry
3-fold dihedral symmetry (group D3, order 6). (Friedman's page says: fully symmetric.)
Minimal triangles
33 triangles tied (within relative 10−9) at the minimal area, in 6 congruence classes:
| count | side lengths | triangles (point indices) | |
|---|---|---|---|
| 6 | 0.1439 · 0.2858 · 0.3988 |
(0,5,9) (0,6,9) (1,4,15) (2,8,16) (4,7,15) (8,16,17) | |
| 6 | 0.2421 · 0.3031 · 0.5335 |
(1,13,14) (2,10,12) (3,6,11) (3,14,17) (5,12,13) (7,10,11) | |
| 6 | 0.2858 · 0.4438 · 0.7247 |
(0,6,7) (1,15,17) (1,16,17) (2,5,8) (2,5,9) (4,6,7) | |
| 6 | 0.3210 · 0.5335 · 0.8515 |
(1,2,13) (1,3,6) (2,6,10) (3,7,17) (5,7,10) (5,13,17) | |
| 6 | 0.3210 · 0.7485 · 1.0678 |
(0,1,3) (2,13,15) (3,7,16) (4,5,10) (6,8,10) (9,13,17) | |
| 3 | 0.5006 · 0.5006 · 0.9993 |
(0,4,11) (8,9,12) (14,15,16) |
Provenance
- Found by Nathan Sudermann-Merx, August 2026.
- Coordinates reconstructed by local optimization:
heilbronn-site reconstruct/reconstruct.py— re-polished from the published record figure — the record holder's arrangement with re-derived coordinates. - Verified in exact arithmetic: all 816 triples enumerated, 33 tied at the minimum.
- Friedman's page lists:
A = .01489+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
