Triangle, n = 6 proven reconstructed coords

A =

\frac{1}{8}

= 0.125000000000000000000000000000000000000000000…

6 minimal triangles in 1 congruence classes, colored by class.

Symmetry

3-fold dihedral symmetry (group D3, order 6). (Friedman's page says: horizontally symmetric.)

6 triangles tied (within relative 10⁻⁹) at the minimal area:

	count	side lengths	triangles (point indices)
	6	`0.3799 · 0.7598 · 1.0052`	(0,1,5) (0,2,4) (0,4,5) (1,2,3) (1,3,5) (2,3,4)

Found by L. Yang, J. Z. Zhang, and Z. B. Zeng, 1991.
Proved optimal by L. Yang, J. Z. Zhang, and Z. B. Zeng, 1994.
One of an infinite family of solutions.
Coordinates reconstructed by local optimization: heilbronn-site reconstruct/reconstruct.py — reconstructed by local optimization; matches published value 0.125.
Verified in exact arithmetic: all 20 triples enumerated, 6 tied at the minimum.
Friedman's page lists: A = 1/8 = .125.

L. Yang, J. Z. Zhang, Z. B. Zeng, A conjecture on the first several Heilbronn numbers and a computation, Chinese Ann. Math. Ser. A 13 (1992) 503–515