Convex, n = 6 proven

A =

\frac{1}{6}

= 0.166666666666666666666666666666666666666666667…

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

Symmetry

6-fold dihedral symmetry (group D6, order 12).

6 points in 1 orbit (6) — hover a point to see its orbit.

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

	count	side lengths	triangles (point indices)
	6	`1.0000 · 1.0000 · 1.7321`	(0,1,2) (0,1,5) (0,4,5) (1,2,3) (2,3,4) (3,4,5)

Found by David Cantrell, June 2007.
Proved optimal by Andreas Dress, Lu Yang, and Zhenbing Zeng, 1995.
The configuration is Cantrell's (2007); the value itself was settled in 1995 — Dress, Yang and Zeng proved that any six points in a convex body K span a triangle of area at most |K|/6, and that 1/6 is sharp.
Coordinates generated from the exact construction: data/sources/exact/constructions.py — regular hexagon.
Verified in exact arithmetic: all 20 triples enumerated, 6 tied at the minimum.