Square, n = 23 record
A = 0.009757289713314…
full precision
Exact value of the published coordinate literals:
0.00975728971331477225716070200657
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
40 triangles tied (within relative 10−9) at the minimal area, in 40 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1697 · 0.2110 · 0.3652 |
(11,13,21) |
| 1 | 0.1791 · 0.2108 · 0.3757 |
(1,6,7) |
| 1 | 0.1933 · 0.2519 · 0.4360 |
(10,19,21) |
| 1 | 0.1933 · 0.3298 · 0.5173 |
(17,19,21) |
| 1 | 0.1758 · 0.3518 · 0.5216 |
(9,10,13) |
| 1 | 0.1361 · 0.3943 · 0.5234 |
(5,18,20) |
| 1 | 0.2415 · 0.2970 · 0.5334 |
(9,11,22) |
| 1 | 0.2167 · 0.3304 · 0.5421 |
(1,2,14) |
| 1 | 0.2400 · 0.3429 · 0.5789 |
(7,9,12) |
| 1 | 0.0952 · 0.5120 · 0.6005 |
(0,16,18) |
| 1 | 0.1758 · 0.4358 · 0.6075 |
(2,10,13) |
| 1 | 0.2108 · 0.4422 · 0.6498 |
(1,3,7) |
| 1 | 0.2498 · 0.4202 · 0.6673 |
(2,4,12) |
| 1 | 0.2381 · 0.4335 · 0.6688 |
(2,8,11) |
| 1 | 0.1895 · 0.4895 · 0.6759 |
(16,20,22) |
| 1 | 0.2738 · 0.4149 · 0.6862 |
(2,3,21) |
| 1 | 0.3126 · 0.3766 · 0.6868 |
(1,4,20) |
| 1 | 0.2507 · 0.4948 · 0.7434 |
(12,14,20) |
| 1 | 0.2531 · 0.5440 · 0.7953 |
(10,15,20) |
| 1 | 0.2512 · 0.5470 · 0.7965 |
(3,6,14) |
| 1 | 0.3576 · 0.4448 · 0.8010 |
(0,6,20) |
| 1 | 0.3695 · 0.4614 · 0.8296 |
(4,9,19) |
| 1 | 0.4005 · 0.4345 · 0.8337 |
(0,9,15) |
| 1 | 0.3943 · 0.4448 · 0.8378 |
(6,18,20) |
| 1 | 0.2688 · 0.5728 · 0.8402 |
(6,15,22) |
| 1 | 0.2386 · 0.6153 · 0.8524 |
(2,9,20) |
| 1 | 0.3437 · 0.5494 · 0.8919 |
(11,14,16) |
| 1 | 0.2781 · 0.6198 · 0.8966 |
(1,12,22) |
| 1 | 0.3591 · 0.5641 · 0.9221 |
(12,13,17) |
| 1 | 0.3298 · 0.6165 · 0.9453 |
(8,17,21) |
| 1 | 0.2970 · 0.6688 · 0.9648 |
(8,11,22) |
| 1 | 0.1697 · 0.7965 · 0.9647 |
(0,13,21) |
| 1 | 0.3652 · 0.6143 · 0.9787 |
(5,11,21) |
| 1 | 0.2083 · 0.7913 · 0.9984 |
(4,6,16) |
| 1 | 0.3298 · 0.6862 · 1.0151 |
(3,17,21) |
| 1 | 0.3741 · 0.6552 · 1.0286 |
(14,15,18) |
| 1 | 0.2083 · 0.8430 · 1.0502 |
(4,6,10) |
| 1 | 0.3345 · 0.7190 · 1.0528 |
(7,10,11) |
| 1 | 0.3621 · 0.7592 · 1.1208 |
(5,15,17) |
| 1 | 0.4527 · 0.7964 · 1.2487 |
(8,9,18) |
Provenance
- Found by Rob Gardiner, September 2026.
- Coordinates by an external contributor, re-verified here:
Rob Gardiner, Heilbronn square configurations, September 2026.— Search from random starting configurations. - Verified in exact arithmetic: all 1771 triples enumerated, 40 tied at the minimum.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
