Great disdyakis dodecahedron

The great disdyakis dodecahedron is a uniform dual polyhedron. It consists of 48 scalene triangles.

If its dual, the great cubicuboctahedron, has an edge length of 1, then the short edges of the triangles will measure $$3\frac{\sqrt{6\left(2-\sqrt2\right)}}{7} ≈ 0.80347$$, the medium edges will be $$2\frac{\sqrt{3\left(10+\sqrt2\right)}}{7} ≈ 1.67192$$, and the long edges will be $$2\frac{\sqrt{6\left(10-\sqrt2\right)}}{7} ≈ 2.05068$$. The triangles have one interior angle of $$\arccos\left(\frac34+\frac{\sqrt2}{8}\right) ≈ 22.06219°$$, one of $$\arccos\left(-\frac16-\frac{\sqrt2}{12}\right) ≈ 106.53003°$$, and one of $$\arccos\left(-\frac{1}{12}+\frac{\sqrt2}{2}\right) ≈ 51.40778°$$.

Vertex coordinates
A great disdyakis dodecahedron with dual edge length 1 has vertex coordinates given by all permutations of:
 * $$\left(±3\frac{3\sqrt2-2}{7},\,0,\,0\right),$$
 * $$\left(±3\frac{2\sqrt2-1}{7},\,±3\frac{2\sqrt2-1}{7},\,0\right),$$
 * $$\left(±\sqrt2,\,±\sqrt2,\,±\sqrt2\right).$$