Square, n = 26 record reconstructed coords

A = 0.006826850040207…

full precision

Exact value of the published coordinate literals: 0.0068268500402073982135822880095

39 triangles tie for the minimal area.

Symmetry

Not symmetric (group C1, order 1).

Minimal triangles

39 triangles tied (within relative 10⁻⁹) at the minimal area, in 21 congruence classes:

count	side lengths	triangles (point indices)
2	`0.1502 · 0.2949 · 0.4402`	(4,7,10) (11,13,17)
2	`0.1774 · 0.3172 · 0.4912`	(3,8,12) (8,12,15)
2	`0.1767 · 0.4402 · 0.6149`	(0,4,10) (6,11,17)
2	`0.2565 · 0.3604 · 0.6153`	(3,10,16) (15,17,20)
2	`0.1385 · 0.5351 · 0.6717`	(4,8,18) (11,12,14)
2	`0.2040 · 0.5016 · 0.7043`	(7,16,19) (13,20,25)
2	`0.3553 · 0.3741 · 0.7285`	(0,12,17) (6,8,10)
2	`0.3993 · 0.4000 · 0.7985`	(7,14,25) (13,18,19)
2	`0.3588 · 0.4541 · 0.8122`	(0,3,5) (6,15,24)
2	`0.1521 · 0.6717 · 0.8227`	(4,18,20) (11,14,16)
2	`0.2729 · 0.6206 · 0.8929`	(1,8,11) (4,12,22)
2	`0.3508 · 0.5524 · 0.9026`	(5,16,25) (19,20,24)
2	`0.4118 · 0.5021 · 0.9135`	(4,13,24) (5,7,11)
2	`0.2685 · 0.6478 · 0.9157`	(1,14,20) (16,18,22)
2	`0.3588 · 0.5798 · 0.9382`	(2,3,5) (2,15,24)
2	`0.1767 · 0.7628 · 0.9388`	(0,4,16) (6,11,20)
2	`0.2040 · 0.7628 · 0.9662`	(4,16,19) (11,20,25)
2	`0.3508 · 0.6580 · 1.0084`	(1,16,25) (19,20,22)
1	`0.1473 · 0.1473 · 0.2776`	(0,2,6)
1	`0.2333 · 0.2799 · 0.5104`	(12,13,21)
1	`0.1921 · 0.5301 · 0.7210`	(14,21,24)

Provenance

Found by Nathan Sudermann-Merx, August 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 2600 triples enumerated, 39 tied at the minimum.
Friedman's page lists: A = .006826+.

Downloads

points.txt coordinates, tab-separated
points.csv coordinates, CSV
points.json full record: value, provenance, verification
figure.svg this figure