Square, n = 4 trivial

A =

\frac{1}{2}

= 0.500000000000000000000000000000000000000000000…

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

Symmetry

4-fold dihedral symmetry (group D4, order 8). (Friedman's page says: completely symmetric.)

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

	count	side lengths	triangles (point indices)
	4	`1.0000 · 1.0000 · 1.4142`	(0,1,2) (0,1,3) (0,2,3) (1,2,3)

Trivial configuration.
Coordinates from spiralulam/heilbronn (MIT): spiralulam/heilbronn config_n04.json — trivial.
Verified in exact arithmetic: all 4 triples enumerated, 4 tied at the minimum.
Friedman's page lists: A = 1/2 = .5.