Square, n = 30 record
A = 0.005445123082749…
full precision
Exact value of the published coordinate literals:
0.005445123082749145488551334146
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
54 triangles tied (within relative 10−9) at the minimal area, in 54 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1194 · 0.1486 · 0.2537 |
(22,26,28) |
| 1 | 0.1327 · 0.1504 · 0.2715 |
(21,25,29) |
| 1 | 0.1682 · 0.2818 · 0.4472 |
(14,18,24) |
| 1 | 0.1566 · 0.3471 · 0.5015 |
(7,12,14) |
| 1 | 0.2508 · 0.3298 · 0.5794 |
(4,7,10) |
| 1 | 0.1813 · 0.4472 · 0.6273 |
(14,24,27) |
| 1 | 0.2767 · 0.3570 · 0.6327 |
(14,16,20) |
| 1 | 0.2884 · 0.3465 · 0.6339 |
(27,28,29) |
| 1 | 0.1860 · 0.4566 · 0.6416 |
(0,5,11) |
| 1 | 0.2763 · 0.3698 · 0.6452 |
(12,19,27) |
| 1 | 0.1878 · 0.4773 · 0.6640 |
(1,4,12) |
| 1 | 0.1805 · 0.4941 · 0.6736 |
(6,9,20) |
| 1 | 0.2460 · 0.4566 · 0.7018 |
(5,11,13) |
| 1 | 0.3166 · 0.4051 · 0.7211 |
(14,19,23) |
| 1 | 0.3698 · 0.3746 · 0.7438 |
(0,12,19) |
| 1 | 0.2518 · 0.4934 · 0.7446 |
(13,15,24) |
| 1 | 0.3720 · 0.3753 · 0.7468 |
(6,8,12) |
| 1 | 0.3785 · 0.3786 · 0.7565 |
(1,11,20) |
| 1 | 0.3808 · 0.3809 · 0.7611 |
(15,19,22) |
| 1 | 0.2884 · 0.4760 · 0.7639 |
(25,27,28) |
| 1 | 0.3594 · 0.4078 · 0.7667 |
(8,15,29) |
| 1 | 0.3465 · 0.4226 · 0.7685 |
(26,27,29) |
| 1 | 0.3862 · 0.3877 · 0.7733 |
(7,16,28) |
| 1 | 0.1482 · 0.6541 · 0.8016 |
(10,15,17) |
| 1 | 0.3193 · 0.4892 · 0.8080 |
(0,4,6) |
| 1 | 0.1498 · 0.6591 · 0.8082 |
(5,20,23) |
| 1 | 0.3147 · 0.4984 · 0.8127 |
(1,9,21) |
| 1 | 0.1572 · 0.6709 · 0.8274 |
(9,11,18) |
| 1 | 0.3252 · 0.5090 · 0.8337 |
(22,24,29) |
| 1 | 0.2497 · 0.5848 · 0.8340 |
(3,10,24) |
| 1 | 0.3491 · 0.4888 · 0.8374 |
(21,23,28) |
| 1 | 0.1483 · 0.6934 · 0.8410 |
(4,8,24) |
| 1 | 0.2655 · 0.5794 · 0.8444 |
(2,4,10) |
| 1 | 0.3301 · 0.5168 · 0.8464 |
(0,10,22) |
| 1 | 0.2735 · 0.5901 · 0.8632 |
(5,18,26) |
| 1 | 0.1359 · 0.7366 · 0.8718 |
(5,7,27) |
| 1 | 0.2775 · 0.5964 · 0.8735 |
(2,15,23) |
| 1 | 0.4382 · 0.4382 · 0.8761 |
(2,13,25) |
| 1 | 0.2723 · 0.6493 · 0.9212 |
(3,5,6) |
| 1 | 0.1572 · 0.7658 · 0.9224 |
(9,11,14) |
| 1 | 0.3341 · 0.5911 · 0.9249 |
(3,18,28) |
| 1 | 0.4207 · 0.5077 · 0.9281 |
(13,20,28) |
| 1 | 0.2460 · 0.7133 · 0.9589 |
(3,11,13) |
| 1 | 0.4617 · 0.5039 · 0.9653 |
(6,15,27) |
| 1 | 0.3553 · 0.6113 · 0.9664 |
(2,17,29) |
| 1 | 0.3477 · 0.6272 · 0.9746 |
(3,12,23) |
| 1 | 0.1805 · 0.7950 · 0.9751 |
(6,9,24) |
| 1 | 0.2008 · 0.7772 · 0.9776 |
(4,18,22) |
| 1 | 0.2763 · 0.7075 · 0.9835 |
(3,19,27) |
| 1 | 0.2518 · 0.7549 · 1.0065 |
(13,15,26) |
| 1 | 0.3471 · 0.6640 · 1.0109 |
(1,12,14) |
| 1 | 0.2931 · 0.7571 · 1.0500 |
(2,20,27) |
| 1 | 0.3275 · 0.8346 · 1.1619 |
(3,15,21) |
| 1 | 0.3328 · 0.8568 · 1.1894 |
(1,19,28) |
Provenance
- Found by Nathan Sudermann-Merx, August 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims-2026-08-20/square-n30. - Verified in exact arithmetic: all 4060 triples enumerated, 54 tied at the minimum.
- Friedman's page lists:
A = .005436+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
