Square, n = 21 record
A = 0.010814929542582…
full precision
Exact value of the published coordinate literals:
0.010814929542582185403049909767
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
36 triangles tied (within relative 10−9) at the minimal area, in 36 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1456 · 0.1821 · 0.2916 |
(1,5,20) |
| 1 | 0.1598 · 0.1798 · 0.3094 |
(0,4,17) |
| 1 | 0.1391 · 0.2079 · 0.3178 |
(7,15,16) |
| 1 | 0.1924 · 0.3131 · 0.4975 |
(6,9,14) |
| 1 | 0.1598 · 0.3601 · 0.5117 |
(0,17,19) |
| 1 | 0.2479 · 0.2996 · 0.5416 |
(2,6,19) |
| 1 | 0.2042 · 0.3702 · 0.5689 |
(2,10,18) |
| 1 | 0.3027 · 0.3335 · 0.6325 |
(1,9,12) |
| 1 | 0.1821 · 0.4879 · 0.6660 |
(5,6,20) |
| 1 | 0.3194 · 0.3989 · 0.7157 |
(2,5,14) |
| 1 | 0.1798 · 0.5453 · 0.7218 |
(4,7,17) |
| 1 | 0.3606 · 0.3702 · 0.7283 |
(2,10,17) |
| 1 | 0.1924 · 0.5501 · 0.7395 |
(1,6,14) |
| 1 | 0.2042 · 0.5443 · 0.7457 |
(2,8,18) |
| 1 | 0.2724 · 0.4879 · 0.7580 |
(5,6,18) |
| 1 | 0.1993 · 0.5631 · 0.7597 |
(1,3,16) |
| 1 | 0.2702 · 0.4975 · 0.7654 |
(6,9,11) |
| 1 | 0.3601 · 0.4178 · 0.7759 |
(0,18,19) |
| 1 | 0.2079 · 0.6023 · 0.8079 |
(7,10,15) |
| 1 | 0.2439 · 0.5942 · 0.8361 |
(1,7,11) |
| 1 | 0.3853 · 0.4548 · 0.8385 |
(12,13,16) |
| 1 | 0.3178 · 0.5298 · 0.8459 |
(15,16,17) |
| 1 | 0.2392 · 0.6182 · 0.8555 |
(0,10,14) |
| 1 | 0.3114 · 0.5558 · 0.8656 |
(4,11,13) |
| 1 | 0.3690 · 0.5069 · 0.8745 |
(5,10,12) |
| 1 | 0.2774 · 0.6176 · 0.8935 |
(8,10,16) |
| 1 | 0.4548 · 0.4683 · 0.9220 |
(12,13,18) |
| 1 | 0.2886 · 0.6405 · 0.9278 |
(13,15,20) |
| 1 | 0.3178 · 0.6129 · 0.9294 |
(0,15,16) |
| 1 | 0.2656 · 0.6860 · 0.9502 |
(12,14,17) |
| 1 | 0.3690 · 0.5942 · 0.9620 |
(7,11,20) |
| 1 | 0.2702 · 0.7159 · 0.9848 |
(9,11,18) |
| 1 | 0.3014 · 0.7384 · 1.0388 |
(3,13,19) |
| 1 | 0.4564 · 0.6176 · 1.0733 |
(8,16,19) |
| 1 | 0.3600 · 0.8343 · 1.1936 |
(0,9,20) |
| 1 | 0.4683 · 0.7408 · 1.2086 |
(3,12,18) |
Provenance
- Found by Tej Stead, August 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims-2026-07-25/square-n21. - Verified in exact arithmetic: all 1330 triples enumerated, 36 tied at the minimum.
- Friedman's page lists:
A = .010814+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
