Great stellapentakis dodecahedron

The great stellapentakis dodecahedron is a uniform dual polyhedron. It consists of 60 isosceles triangles.

If its dual, the truncated great icosahedron, has an edge length of 1, then the short edges of the triangles will measure $$9\frac{1+2\sqrt5}{19} ≈ 2.59206$$, and the long edges will be $$3\frac{1+\sqrt5}{2} ≈ 4.85410$$. The triangles have two interior angles of $$\arccos\left(\frac34+\frac{\sqrt5}{12}\right) ≈ 20.55444°$$, one of $$\arccos\left(-\frac{7}{36}-\frac{\sqrt5}{4}\right) ≈ 138.89111°$$.

Vertex coordinates
A great stellapentakis dodecahedron with dual edge length 1 has vertex coordinates given by all even permutations of:
 * $$\left(±3\frac{\sqrt5-1}{4},\,±3\frac{1+\sqrt5}{4},\,0\right),$$
 * $$\left(±9\frac{9-\sqrt5}{76},\,±9\frac{5\sqrt5-7}{76},\,0\right),$$
 * $$\left(±\frac32,\,±\frac32,\,±\frac32\right).$$