Truncated dodecahedron

The truncated dodecahedron, or tid, is one of the 13 Archimedean solids. It consists of 20 triangles and 12 decagons. Each vertex joins one triangle and two decagons. As the name suggests, it can be obtained by truncation of the dodecahedron.

Vertex coordinates
A truncated cube of edge length 1 has vertex coordinates given by all even permutations and sign changes of ic|2}})/2, ±(1+$\sqrt{(37+15√5)/8}$)/2, ±1/2).
 * (0, ±1/2, ±(5+3$\sqrt{5}$)/4)
 * (±1/2, ±(3+$\sqrt{(5+√5)/2}$)/4, ±(3+$\sqrt{(5+√5)/2}$)/2)
 * (±(3+$\sqrt{(5+2√5)/15}$)/4, ±(1+$\sqrt{5}$)/2, ±(2+$\sqrt{2}$)/2)