Convex, n = 5 record

A =

\frac{5 - \sqrt{5}}{10}

= 0.276393202250021030359082633126872376455938164…

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

Symmetry

5-fold dihedral symmetry (group D5, order 10).

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

	count	side lengths	triangles (point indices)
	5	`1.1756 · 1.1756 · 1.9021`	(0,1,2) (0,1,4) (0,3,4) (1,2,3) (2,3,4)

Found by David Cantrell, June 2007.
Coordinates generated from the exact construction: data/sources/exact/constructions.py — regular pentagon.
Verified in exact arithmetic: all 10 triples enumerated, 5 tied at the minimum.
Friedman's page lists: A = (5 - √5) / 10 = .276+.