Medial disdyakis triacontahedron

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

If its dual, the quasitruncated dodecadodecahedron, has an edge length of 1, then the triangle's short edges will be $$5\frac{3\sqrt2-\sqrt{10}}{6} ≈ 0.90030$$, the medium edges will be $$5\frac{3\sqrt2+\sqrt{10}}{6} ≈ 6.17077$$, and the long edges will be $$2\sqrt{10} ≈ 6.32456$$. The triangles have one interior angle of $$\arccos\left(-\frac{1}{10}\right) ≈ 95.73917°$$, one of $$\arccos\left(\frac38+\frac{11\sqrt5}{40}\right) ≈ 8.14257°$$, and one of $$\arccos\left(-\frac38+\frac{11\sqrt5}{40}\right) ≈ 76.11829°$$.

Vertex coordinates
A medial disdyakis triacontahedron with dual edge length 1 has vertex coordinates given by all even permutations of:
 * $$\left(±\frac{5+3\sqrt5}{2},\,±\frac{5+\sqrt5}{2},\,0\right),$$
 * $$\left(±\frac53,\,0,\,0\right),$$
 * $$\left(±\frac{5-\sqrt5}{2},\,±\frac{3\sqrt5-5}{2},\,0\right),$$
 * $$\left(±5\frac{\sqrt5-1}{12},\,±\frac56,\,±5\frac{1+\sqrt5}{12}\right).$$