Augmented dodecahedron (Johnson solid)

The augmented dodecahedron is one of the 92 Johnson solids (J58). It consists of 5 triangles and 1+5+5 pentagons. It can be constructed by attaching a pentagonal pyramid to one of the faces of the regular dodecahedron.

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