Triangle, n = 4 proven

A =

\frac{1}{3}

= 0.333333333333333333333333333333333333333333333…

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

Symmetry

3-fold dihedral symmetry (group D3, order 6).

4 points in 2 orbits (3 + 1) — hover a point to see its orbit.

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

	count	side lengths	triangles (point indices)
	3	`0.8774 · 0.8774 · 1.5197`	(0,1,3) (0,2,3) (1,2,3)

Trivial configuration.
Coordinates generated from the exact construction: data/sources/exact/constructions.py — vertices plus centroid.
Verified in exact arithmetic: all 4 triples enumerated, 3 tied at the minimum.