Great triakis icosahedron

The great triakis icosahedron is a uniform dual polyhedron. It consists of 60 isosceles triangles.

If its dual, the quasitruncated great stellated dodecahedron, has an edge length of 1, then the short edges of the triangles will measure $$5\frac{7-\sqrt5}{22} ≈ 1.08271$$, and the long edges will be $$\frac{5-\sqrt5}{2} ≈ 1.38197$$. The triangles have two interior angles of $$\arccos\left(\frac34-\frac{\sqrt5}{20}\right) ≈ 50.34252°$$, and one of $$\arccos\left(-\frac{3}{20}+\frac{3\sqrt5}{20}\right) ≈ 79.31495°$$.

Vertex coordinates
A great triakis icosahedron with dual edge length 1 has vertex coordinates given by all even permutations of:
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,0\right),$$
 * $$\left(±5\frac{13-5\sqrt5}{44},\,±5\frac{7-\sqrt5}{44},\,0\right),$$
 * $$\left(±5\frac{2\sqrt5-3}{22},\,±5\frac{2\sqrt5-3}{22},\,±5\frac{2\sqrt5-3}{22}\right).$$