Triaugmented dodecahedron

The triaugmented dodecahedron is one of the 92 Johnson solids (J61). It consists of 3+6+6 triangles and 3+3+3 pentagons. It can be constructed by attaching pentagonal pyramids to three mutually non-adjacent faces of the regular dodecahedron.

Vertex coordinates
A triaugmented dodecahedron of edge length 1 has vertices given by all even permutations of: As well as:
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac12,\,0\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(0,\,\frac{15+\sqrt5}{20},\,±\frac{5+4\sqrt5}{10}\right),$$
 * $$\left(\frac{15+\sqrt5}{20},\,-\frac{5+4\sqrt5}{10},\,0\right).$$