Square, n = 25 record
A = 0.007244675860134…
full precision
Exact value of the published coordinate literals:
0.007244675860134368323908718912
Symmetry
Not symmetric (group C1, order 1). The record configuration is listed as: not symmetric.
Minimal triangles
41 triangles tied (within relative 10−9) at the minimal area, in 41 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1436 · 0.1714 · 0.2997 |
(0,3,6) |
| 1 | 0.1513 · 0.1647 · 0.3009 |
(6,11,12) |
| 1 | 0.1493 · 0.1680 · 0.3024 |
(0,5,8) |
| 1 | 0.2656 · 0.2929 · 0.5561 |
(5,12,14) |
| 1 | 0.2569 · 0.3516 · 0.6065 |
(16,18,20) |
| 1 | 0.1680 · 0.4528 · 0.6185 |
(0,5,10) |
| 1 | 0.1647 · 0.4752 · 0.6378 |
(6,11,18) |
| 1 | 0.2660 · 0.3961 · 0.6606 |
(1,9,13) |
| 1 | 0.2667 · 0.3971 · 0.6623 |
(20,21,23) |
| 1 | 0.1731 · 0.5002 · 0.6715 |
(14,20,24) |
| 1 | 0.1513 · 0.5347 · 0.6841 |
(11,12,13) |
| 1 | 0.1462 · 0.5540 · 0.6983 |
(8,17,20) |
| 1 | 0.1874 · 0.5127 · 0.6985 |
(7,15,19) |
| 1 | 0.3659 · 0.3787 · 0.7436 |
(6,8,10) |
| 1 | 0.1959 · 0.5627 · 0.7574 |
(4,9,17) |
| 1 | 0.1540 · 0.6144 · 0.7669 |
(10,14,16) |
| 1 | 0.3864 · 0.3877 · 0.7732 |
(0,12,18) |
| 1 | 0.1541 · 0.6207 · 0.7733 |
(2,7,18) |
| 1 | 0.3839 · 0.4119 · 0.7950 |
(7,13,24) |
| 1 | 0.3199 · 0.4793 · 0.7982 |
(0,2,4) |
| 1 | 0.3897 · 0.4119 · 0.8007 |
(14,17,19) |
| 1 | 0.3925 · 0.4128 · 0.8045 |
(4,7,12) |
| 1 | 0.1608 · 0.6841 · 0.8438 |
(11,13,15) |
| 1 | 0.1493 · 0.6983 · 0.8464 |
(5,8,20) |
| 1 | 0.2632 · 0.6108 · 0.8732 |
(3,11,21) |
| 1 | 0.2899 · 0.6294 · 0.9186 |
(1,8,11) |
| 1 | 0.3472 · 0.5794 · 0.9260 |
(4,15,24) |
| 1 | 0.1622 · 0.7669 · 0.9282 |
(9,10,16) |
| 1 | 0.3839 · 0.5459 · 0.9292 |
(2,13,24) |
| 1 | 0.1647 · 0.7764 · 0.9402 |
(6,11,20) |
| 1 | 0.2813 · 0.6606 · 0.9413 |
(1,13,20) |
| 1 | 0.2810 · 0.6638 · 0.9442 |
(15,17,23) |
| 1 | 0.1680 · 0.7811 · 0.9483 |
(0,5,15) |
| 1 | 0.1731 · 0.7764 · 0.9487 |
(11,20,24) |
| 1 | 0.2929 · 0.6627 · 0.9551 |
(5,12,23) |
| 1 | 0.1836 · 0.7733 · 0.9562 |
(2,18,21) |
| 1 | 0.1874 · 0.7811 · 0.9678 |
(5,15,19) |
| 1 | 0.2843 · 0.6949 · 0.9786 |
(1,2,6) |
| 1 | 0.3556 · 0.6623 · 1.0175 |
(19,20,23) |
| 1 | 0.2991 · 0.7228 · 1.0214 |
(0,16,23) |
| 1 | 0.3459 · 1.0007 · 1.3464 |
(4,10,23) |
Provenance
- Found by Nathan Sudermann-Merx, August 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims-2026-08-20/square-n25. - Verified in exact arithmetic: all 2300 triples enumerated, 41 tied at the minimum.
- Friedman's page lists:
A = .007327+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
