Square, n = 26 record

A = 0.007577591009829…

full precision

Exact value of the published coordinate literals: 0.00757759100982904547778149636451

50 triangles tie for the minimal area.

Symmetry

180° Rotationally symmetric (group C2, order 2).

26 points in 13 orbits (2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2) — hover a point to see its orbit.

Minimal triangles

50 triangles tied (within relative 10⁻⁹) at the minimal area, in 25 congruence classes:

count	side lengths	triangles (point indices)
2	`0.1435 · 0.3690 · 0.5082`	(8,16,21) (9,17,20)
2	`0.2309 · 0.3323 · 0.5605`	(12,14,24) (13,15,25)
2	`0.2413 · 0.3371 · 0.5759`	(4,10,21) (5,11,20)
2	`0.2448 · 0.3371 · 0.5795`	(4,6,21) (5,7,20)
2	`0.2732 · 0.3264 · 0.5974`	(8,9,24) (8,9,25)
2	`0.2780 · 0.3923 · 0.6688`	(4,14,16) (5,15,17)
2	`0.2833 · 0.4211 · 0.7031`	(0,17,18) (1,16,19)
2	`0.1963 · 0.5112 · 0.7058`	(2,16,22) (3,17,23)
2	`0.3729 · 0.3741 · 0.7459`	(0,13,22) (1,12,23)
2	`0.2164 · 0.5379 · 0.7531`	(0,2,21) (1,3,20)
2	`0.2331 · 0.5653 · 0.7973`	(2,9,13) (3,8,12)
2	`0.3264 · 0.4838 · 0.8093`	(8,9,22) (8,9,23)
2	`0.2331 · 0.6027 · 0.8349`	(2,9,11) (3,8,10)
2	`0.2309 · 0.6139 · 0.8438`	(4,13,15) (5,12,14)
2	`0.3729 · 0.4818 · 0.8540`	(0,11,22) (1,10,23)
2	`0.2732 · 0.5974 · 0.8698`	(8,24,25) (9,24,25)
2	`0.3381 · 0.5759 · 0.9134`	(4,10,22) (5,11,23)
2	`0.3356 · 0.5795 · 0.9145`	(6,12,21) (7,13,20)
2	`0.2144 · 0.7205 · 0.9341`	(2,19,20) (3,18,21)
2	`0.3221 · 0.6185 · 0.9400`	(6,11,15) (7,10,14)
2	`0.1435 · 0.7977 · 0.9402`	(6,17,20) (7,16,21)
2	`0.3602 · 0.6465 · 1.0062`	(8,11,14) (9,10,15)
2	`0.4420 · 0.5653 · 1.0069`	(8,12,20) (9,13,21)
2	`0.2317 · 0.7945 · 1.0256`	(18,22,25) (19,23,24)
2	`0.4838 · 0.8093 · 1.2928`	(8,22,23) (9,22,23)

Provenance

Found by Fable 5.1 with Shengtong Zhang, September 2026.
Coordinates by an external contributor, re-verified here: Fable51 search campaign, September 2026: symmetry-reduced basin hopping (orbit parametrization, ruin-and-recreate, soft-min L-BFGS warm-up, trust-region SLP polish); tie system refined to 80 digits by damped Gauss-Newton; verified in exact rational arithmetic — C2 (180° rotational) symmetric, 50 tied minimal triangles; D2-restricted optimum, then C2 basin hopping.
Verified in exact arithmetic: all 2600 triples enumerated, 50 tied at the minimum.

Record history

2026-08-21 .007078+ — Nathan Sudermann-Merx (coordinates never published)

Downloads

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