Metabiaugmented dodecahedron

The metabiaugmented dodecahedron, or mabaud, is one of the 92 Johnson solids (J60). It consists of 2+4+4 triangles and 2+2+2+4 pentagons. It can be constructed by attaching pentagonal pyramids to two non-opposite, non-adjacent faces of the regular dodecahedron.

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