Great disdyakis triacontahedron

The great disdyakis triacontahedron is a uniform dual polyhedron. It consists of 120 scalene triangles.

If its dual, the great quasitruncated icosidodecahedron, has an edge length of 1, then the triangle faces' short edges will measure $$3\frac{\sqrt{15\left(65-19\sqrt5\right)}}{55} ≈ 1.00239$$, the medium edges will be $$2\frac{\sqrt{15\left(5+\sqrt5\right)}}{5} ≈ 4.16732$$, and the long edges will be $$\frac{\sqrt{15\left(85+31\sqrt5\right)}}{11} ≈ 4.37382$$. The kites have one interior angle of $$\arccos\left(\frac16+\frac{\sqrt5}{15}\right) ≈ 71.59464°$$, one of $$\arccos\left(\frac34+\frac{\sqrt5}{10}\right) ≈ 13.19300°$$, and one of $$\arccos\left(\frac38-\frac{5\sqrt5}{24}\right) ≈ 95.21236°$$.

Vertex coordinates
A great disdyakis triacontahedron with dual edge length 1 has vertex coordinates given by all even permutations of:
 * $$\left(±3\frac{4\sqrt5-5}{11},\,0,\,0\right),$$
 * $$\left(±\frac{5-\sqrt5}{2},\,±\frac{5+\sqrt5}{2},\,0\right),$$
 * $$\left(±3\frac{5-\sqrt5}{10},\,±3\frac{3\sqrt5-5}{10},\,0\right),$$
 * $$\left(±3\frac{25-9\sqrt5}{44},\,±3\frac{4\sqrt5-5}{22},\,±3\frac{15-\sqrt5}{44}\right),$$
 * $$\left(±\sqrt5,\,±\sqrt5,\,±\sqrt5\right).$$