Square, n = 27 record reconstructed coords
A = 0.006790349241367…
full precision
Exact value of the published coordinate literals:
0.0067903492413679419518902513265
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
49 triangles tied (within relative 10−9) at the minimal area, in 49 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1097 · 0.2182 · 0.3148 |
(2,3,20) |
| 1 | 0.1115 · 0.2163 · 0.3148 |
(1,4,23) |
| 1 | 0.1115 · 0.2166 · 0.3152 |
(1,4,25) |
| 1 | 0.1101 · 0.2182 · 0.3152 |
(16,17,26) |
| 1 | 0.1101 · 0.2188 · 0.3158 |
(16,17,21) |
| 1 | 0.1097 · 0.2193 · 0.3160 |
(2,3,24) |
| 1 | 0.2163 · 0.3357 · 0.5496 |
(1,23,24) |
| 1 | 0.2166 · 0.3357 · 0.5500 |
(4,25,26) |
| 1 | 0.2182 · 0.3357 · 0.5516 |
(16,25,26) |
| 1 | 0.2175 · 0.3368 · 0.5521 |
(18,21,22) |
| 1 | 0.2182 · 0.3366 · 0.5525 |
(3,19,20) |
| 1 | 0.2193 · 0.3357 · 0.5527 |
(2,23,24) |
| 1 | 0.2188 · 0.3368 · 0.5533 |
(17,21,22) |
| 1 | 0.2007 · 0.4033 · 0.6021 |
(11,12,19) |
| 1 | 0.2007 · 0.4048 · 0.6036 |
(9,11,21) |
| 1 | 0.2006 · 0.4049 · 0.6036 |
(9,10,20) |
| 1 | 0.2006 · 0.4058 · 0.6046 |
(9,10,25) |
| 1 | 0.2009 · 0.4057 · 0.6047 |
(10,12,24) |
| 1 | 0.2007 · 0.4059 · 0.6047 |
(9,11,23) |
| 1 | 0.2007 · 0.4061 · 0.6049 |
(11,12,26) |
| 1 | 0.2728 · 0.3757 · 0.6471 |
(8,13,18) |
| 1 | 0.2743 · 0.3751 · 0.6480 |
(4,5,6) |
| 1 | 0.2745 · 0.3751 · 0.6482 |
(0,1,7) |
| 1 | 0.2747 · 0.3751 · 0.6484 |
(0,7,17) |
| 1 | 0.2748 · 0.3757 · 0.6491 |
(2,8,13) |
| 1 | 0.2755 · 0.3751 · 0.6492 |
(3,5,6) |
| 1 | 0.2754 · 0.3759 · 0.6499 |
(14,15,16) |
| 1 | 0.1523 · 0.5570 · 0.7077 |
(13,14,19) |
| 1 | 0.1523 · 0.5582 · 0.7090 |
(8,15,22) |
| 1 | 0.1541 · 0.5575 · 0.7101 |
(5,8,20) |
| 1 | 0.1542 · 0.5575 · 0.7101 |
(7,14,21) |
| 1 | 0.1523 · 0.6927 · 0.8439 |
(0,13,19) |
| 1 | 0.1541 · 0.6919 · 0.8450 |
(7,8,20) |
| 1 | 0.1542 · 0.6919 · 0.8451 |
(5,14,21) |
| 1 | 0.1523 · 0.6938 · 0.8451 |
(6,15,22) |
| 1 | 0.1564 · 0.6919 · 0.8473 |
(5,14,23) |
| 1 | 0.1565 · 0.6919 · 0.8474 |
(7,8,25) |
| 1 | 0.1562 · 0.6927 · 0.8478 |
(0,13,26) |
| 1 | 0.1559 · 0.6938 · 0.8487 |
(6,15,24) |
| 1 | 0.2600 · 0.6563 · 0.9157 |
(7,9,19) |
| 1 | 0.2604 · 0.6567 · 0.9165 |
(6,10,21) |
| 1 | 0.2601 · 0.6576 · 0.9171 |
(5,9,22) |
| 1 | 0.2612 · 0.6574 · 0.9180 |
(11,14,24) |
| 1 | 0.2614 · 0.6577 · 0.9185 |
(8,10,26) |
| 1 | 0.2615 · 0.6586 · 0.9195 |
(12,13,25) |
| 1 | 0.2627 · 0.6587 · 0.9208 |
(12,15,23) |
| 1 | 0.4804 · 0.6010 · 1.0810 |
(1,10,19) |
| 1 | 0.4807 · 0.6015 · 1.0820 |
(12,17,20) |
| 1 | 0.4822 · 0.6018 · 1.0837 |
(11,18,25) |
Provenance
- Found by Marc-Emmanuel Coupvent des Graviers, July 2026.
- Coordinates reconstructed by local optimization:
heilbronn-site reconstruct/reconstruct.py— re-polished from the published record figure — the record holder's arrangement with re-derived coordinates. - Verified in exact arithmetic: all 2925 triples enumerated, 49 tied at the minimum.
- Friedman's page lists:
A = .006790+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
