Triaugmented dodecahedron

The triaugmented dodecahedron, or taud, 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:
 * (±(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),
 * (±(5+4$\sqrt{5}$)/10, (15+$\sqrt{5}$)/20, 0).