Convex, n = 4 proven

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).

4 points in 1 orbit (4) — hover a point to see its orbit.

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

	count	side lengths	triangles (point indices)
	4	`1.4142 · 1.4142 · 2.0000`	(0,1,2) (0,1,3) (0,2,3) (1,2,3)

Trivial configuration.
Coordinates generated from the exact construction: data/sources/exact/constructions.py — square (any parallelogram).
Verified in exact arithmetic: all 4 triples enumerated, 4 tied at the minimum.