Parabiaugmented dodecahedron

The parabiaugmented dodecahedron, or pabaud, is one of the 92 Johnson solids (J59). It consists of 10 triangles and 10 pentagons. It can be constructed by attaching pentagonal pyramids to two opposite faces of the regular dodecahedron.

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