Augmented dodecahedron (Johnson solid)

The augmented dodecahedron, or aud, 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:
 * (±(3+$\sqrt{5}$)/4, ±1/2, 0),
 * (±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{(65–2√5)/75}$)/4),
 * (0, (5+4$\sqrt{5}$)/10, (15+$\sqrt{5}$)/20).