Square, n = 29 record
A = 0.005619669469132…
full precision
Exact value of the published coordinate literals:
0.005619669469132689883128216482
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
51 triangles tied (within relative 10−9) at the minimal area, in 51 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1348 · 0.1505 · 0.2731 |
(22,25,27) |
| 1 | 0.1411 · 0.3324 · 0.4706 |
(7,11,14) |
| 1 | 0.1834 · 0.3020 · 0.4830 |
(14,17,24) |
| 1 | 0.2324 · 0.3301 · 0.5611 |
(4,7,9) |
| 1 | 0.2727 · 0.3414 · 0.6131 |
(9,16,24) |
| 1 | 0.1881 · 0.4558 · 0.6427 |
(15,24,27) |
| 1 | 0.2833 · 0.3703 · 0.6527 |
(14,16,20) |
| 1 | 0.1748 · 0.4827 · 0.6564 |
(16,23,28) |
| 1 | 0.1857 · 0.4837 · 0.6683 |
(6,10,20) |
| 1 | 0.1806 · 0.4918 · 0.6714 |
(0,3,12) |
| 1 | 0.1808 · 0.4957 · 0.6754 |
(5,9,19) |
| 1 | 0.1440 · 0.5337 · 0.6765 |
(9,11,15) |
| 1 | 0.2646 · 0.4558 · 0.7196 |
(13,15,24) |
| 1 | 0.3492 · 0.3977 · 0.7463 |
(5,7,12) |
| 1 | 0.3730 · 0.3763 · 0.7487 |
(6,8,11) |
| 1 | 0.3237 · 0.4317 · 0.7547 |
(14,19,23) |
| 1 | 0.3659 · 0.3912 · 0.7565 |
(0,11,19) |
| 1 | 0.3783 · 0.3862 · 0.7640 |
(8,15,28) |
| 1 | 0.3766 · 0.3901 · 0.7661 |
(7,16,27) |
| 1 | 0.3784 · 0.3886 · 0.7665 |
(1,12,20) |
| 1 | 0.3094 · 0.4581 · 0.7669 |
(6,13,26) |
| 1 | 0.3376 · 0.4387 · 0.7758 |
(2,13,21) |
| 1 | 0.1518 · 0.6501 · 0.8011 |
(10,12,17) |
| 1 | 0.3417 · 0.4682 · 0.8094 |
(22,24,28) |
| 1 | 0.3020 · 0.5170 · 0.8185 |
(1,3,5) |
| 1 | 0.1440 · 0.6793 · 0.8226 |
(9,11,18) |
| 1 | 0.3065 · 0.5181 · 0.8241 |
(0,9,22) |
| 1 | 0.2546 · 0.5730 · 0.8271 |
(18,20,25) |
| 1 | 0.3317 · 0.5048 · 0.8360 |
(6,18,28) |
| 1 | 0.1538 · 0.6930 · 0.8461 |
(3,20,23) |
| 1 | 0.2809 · 0.5664 · 0.8469 |
(3,17,25) |
| 1 | 0.3346 · 0.5137 · 0.8479 |
(1,10,21) |
| 1 | 0.2324 · 0.6230 · 0.8550 |
(2,7,9) |
| 1 | 0.3516 · 0.5090 · 0.8602 |
(5,17,27) |
| 1 | 0.3866 · 0.4820 · 0.8683 |
(17,20,21) |
| 1 | 0.2892 · 0.5856 · 0.8744 |
(4,18,26) |
| 1 | 0.4387 · 0.4581 · 0.8964 |
(2,13,26) |
| 1 | 0.2694 · 0.6277 · 0.8967 |
(1,15,23) |
| 1 | 0.4206 · 0.4855 · 0.9057 |
(13,20,27) |
| 1 | 0.1518 · 0.7576 · 0.9087 |
(10,12,14) |
| 1 | 0.3020 · 0.6350 · 0.9366 |
(2,3,5) |
| 1 | 0.2003 · 0.7416 · 0.9415 |
(4,17,22) |
| 1 | 0.1857 · 0.7580 · 0.9432 |
(6,10,24) |
| 1 | 0.1881 · 0.7580 · 0.9457 |
(10,24,27) |
| 1 | 0.1808 · 0.7930 · 0.9733 |
(5,9,23) |
| 1 | 0.2646 · 0.7193 · 0.9836 |
(13,15,25) |
| 1 | 0.3324 · 0.6600 · 0.9922 |
(1,11,14) |
| 1 | 0.4317 · 0.6024 · 1.0338 |
(14,19,26) |
| 1 | 0.3262 · 0.8465 · 1.1724 |
(1,19,27) |
| 1 | 0.3207 · 0.8683 · 1.1888 |
(1,8,25) |
| 1 | 0.3197 · 0.8799 · 1.1994 |
(2,16,22) |
Provenance
- Found by Nathan Sudermann-Merx, August 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims-2026-08-20/square-n29. - Verified in exact arithmetic: all 3654 triples enumerated, 51 tied at the minimum.
- Friedman's page lists:
A = .005569+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
