Square, n = 18 record
A = 0.014432656413084…
full precision
Exact value of the published coordinate literals:
0.0144326564130846427223793085775
Symmetry
Not symmetric (group C1, order 1). The record configuration is listed as: vertically and horizontally symmetric.
Minimal triangles
29 triangles tied (within relative 10−9) at the minimal area, in 29 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1674 · 0.3114 · 0.4603 |
(7,15,16) |
| 1 | 0.1889 · 0.3208 · 0.4952 |
(6,14,17) |
| 1 | 0.2352 · 0.3017 · 0.5254 |
(8,10,13) |
| 1 | 0.2715 · 0.4156 · 0.6816 |
(5,9,13) |
| 1 | 0.3323 · 0.3734 · 0.7008 |
(1,9,12) |
| 1 | 0.3000 · 0.4156 · 0.7108 |
(3,5,11) |
| 1 | 0.3114 · 0.4524 · 0.7599 |
(7,10,15) |
| 1 | 0.2941 · 0.4777 · 0.7678 |
(2,8,17) |
| 1 | 0.3880 · 0.3887 · 0.7732 |
(7,12,13) |
| 1 | 0.3208 · 0.4701 · 0.7874 |
(6,11,14) |
| 1 | 0.2554 · 0.5370 · 0.7885 |
(3,9,14) |
| 1 | 0.2067 · 0.5948 · 0.7972 |
(0,4,7) |
| 1 | 0.2078 · 0.6148 · 0.8186 |
(1,5,6) |
| 1 | 0.3051 · 0.5580 · 0.8603 |
(3,4,15) |
| 1 | 0.2352 · 0.6614 · 0.8936 |
(8,10,16) |
| 1 | 0.2693 · 0.6344 · 0.9011 |
(1,3,16) |
| 1 | 0.2381 · 0.7129 · 0.9484 |
(9,11,17) |
| 1 | 0.4603 · 0.4961 · 0.9545 |
(0,15,16) |
| 1 | 0.3410 · 0.6298 · 0.9689 |
(0,2,6) |
| 1 | 0.2941 · 0.6812 · 0.9731 |
(2,4,17) |
| 1 | 0.2398 · 0.7374 · 0.9747 |
(1,7,11) |
| 1 | 0.4952 · 0.5064 · 1.0000 |
(1,14,17) |
| 1 | 0.3046 · 0.7025 · 1.0052 |
(0,12,14) |
| 1 | 0.2881 · 0.7214 · 1.0075 |
(1,13,15) |
| 1 | 0.3734 · 0.7548 · 1.1269 |
(1,9,10) |
| 1 | 0.3859 · 0.7592 · 1.1438 |
(0,8,11) |
| 1 | 0.2850 · 0.8809 · 1.1645 |
(4,5,8) |
| 1 | 0.3887 · 0.7853 · 1.1729 |
(6,7,13) |
| 1 | 0.4476 · 0.8644 · 1.3112 |
(13,16,17) |
Provenance
- Found by Nathan Sudermann-Merx, August 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims/05-extension-square-n18. - Verified in exact arithmetic: all 816 triples enumerated, 29 tied at the minimum.
- Friedman's page lists:
A = .01459+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
