Triangle, n = 5 proven reconstructed coords

A =

3 - 2 \sqrt{2}

= 0.171572875253809902396622551580603842860656249…

4 minimal triangles in 2 congruence classes, colored by class.

Symmetry

Mirror symmetric (group D1, order 2). (Friedman's page says: horizontally symmetric.)

4 triangles tied (within relative 10⁻⁹) at the minimal area, in 2 congruence classes:

	count	side lengths	triangles (point indices)
	2	`0.5605 · 0.6295 · 0.9352`	(0,1,2) (0,2,3)
	2	`0.5605 · 0.8902 · 1.3532`	(0,3,4) (1,2,4)

Proved optimal by Royce Peng, 1989.
One of an infinite family of solutions.
Coordinates reconstructed by local optimization: heilbronn-site reconstruct/reconstruct.py — reconstructed by local optimization; matches published value 0.171+ and symmetry (Mirror symmetric).
Verified in exact arithmetic: all 10 triples enumerated, 4 tied at the minimum.
Friedman's page lists: A = 3 - 2√2 = .171+.