Square, n = 17 record

A = 0.016481222005777…

full precision

Exact value of the published coordinate literals: 0.0164812220057778171981673202475

29 triangles tie for the minimal area.

Symmetry

Not symmetric (group C1, order 1).

Minimal triangles

29 triangles tied (within relative 10⁻⁹) at the minimal area, in 29 congruence classes:

count	side lengths	triangles (point indices)
1	`0.1383 · 0.2901 · 0.3860`	(0,4,16)
1	`0.1383 · 0.3071 · 0.4087`	(0,10,16)
1	`0.2730 · 0.3170 · 0.5788`	(1,11,13)
1	`0.2730 · 0.3273 · 0.5897`	(1,3,11)
1	`0.2543 · 0.3620 · 0.6062`	(9,11,14)
1	`0.3247 · 0.3803 · 0.6986`	(7,9,13)
1	`0.3549 · 0.4675 · 0.8184`	(0,8,13)
1	`0.2812 · 0.5897 · 0.8671`	(1,3,7)
1	`0.2939 · 0.5788 · 0.8690`	(1,13,15)
1	`0.2593 · 0.6162 · 0.8716`	(0,2,6)
1	`0.2901 · 0.5912 · 0.8777`	(4,7,16)
1	`0.3478 · 0.5364 · 0.8809`	(5,10,12)
1	`0.3071 · 0.5858 · 0.8895`	(0,10,14)
1	`0.3170 · 0.5817 · 0.8954`	(4,11,13)
1	`0.3341 · 0.5815 · 0.9125`	(7,8,10)
1	`0.3470 · 0.5899 · 0.9341`	(2,8,15)
1	`0.2336 · 0.7090 · 0.9390`	(1,5,6)
1	`0.2543 · 0.6891 · 0.9401`	(6,9,11)
1	`0.2543 · 0.6904 · 0.9414`	(2,9,11)
1	`0.2477 · 0.7047 · 0.9491`	(0,7,15)
1	`0.2604 · 0.7129 · 0.9702`	(12,14,16)
1	`0.4087 · 0.5809 · 0.9872`	(6,10,16)
1	`0.3803 · 0.6366 · 1.0146`	(7,13,14)
1	`0.2418 · 0.8314 · 1.0706`	(2,3,13)
1	`0.2730 · 0.8060 · 1.0767`	(4,5,9)
1	`0.4287 · 0.6573 · 1.0842`	(6,12,15)
1	`0.4287 · 0.8504 · 1.2779`	(6,7,12)
1	`0.3710 · 0.9190 · 1.2887`	(0,1,9)
1	`0.4725 · 0.8427 · 1.3141`	(1,8,16)

Provenance

Found by Tej Stead, July 2026.
Coordinates from this site's companion repository: TejSteadQC/heilbronn-configurations claims/04-extension-square-n17.
Verified in exact arithmetic: all 680 triples enumerated, 29 tied at the minimum.
Friedman's page lists: A = .016481+.

Downloads

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