Square, n = 20 record reconstructed coords
A = 0.012911555683941…
full precision
Exact value of the published coordinate literals:
0.012911555683941858938602390276
Symmetry
Symmetry
C4 (group C4, order 4). (Friedman's page says: 180° rotationally symmetric.)
Minimal triangles
36 triangles tied (within relative 10−9) at the minimal area, in 9 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 4 | 0.1599 · 0.2294 · 0.3610 |
(0,3,4) (2,5,8) (11,14,17) (15,16,19) |
| 4 | 0.2623 · 0.4808 · 0.7394 |
(0,1,2) (3,6,14) (5,13,16) (17,18,19) |
| 4 | 0.2823 · 0.4737 · 0.7527 |
(1,4,6) (1,8,13) (6,11,18) (13,15,18) |
| 4 | 0.2294 · 0.5964 · 0.8229 |
(0,4,8) (4,11,14) (5,8,15) (11,15,19) |
| 4 | 0.3610 · 0.5263 · 0.8854 |
(2,3,4) (2,8,16) (3,11,17) (15,16,17) |
| 4 | 0.4291 · 0.4905 · 0.9179 |
(1,9,15) (4,10,18) (6,7,8) (11,12,13) |
| 4 | 0.3610 · 0.5973 · 0.9567 |
(0,11,17) (2,8,19) (3,4,5) (14,15,16) |
| 4 | 0.4198 · 0.6317 · 1.0503 |
(0,9,13) (1,7,14) (5,12,18) (6,10,19) |
| 4 | 0.4643 · 0.6688 · 1.1321 |
(1,10,17) (2,9,18) (3,7,13) (6,12,16) |
Provenance
- Found by William Shanley, 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 1140 triples enumerated, 36 tied at the minimum.
- Friedman's page lists:
A = 0.01291+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
