Parabidiminished rhombicosidodecahedron

The parabidiminished rhombicosidodecahedron is one of the 92 Johnson solids (J80). It consists of 10 triangles, 10+10 squares, 10 pentagons, and 2 decagons. It can be constructed by removing two opposite pentagonal cupolaic caps of the small rhombicosidodecahedron.

Vertex coordinates
A parabidiminished rhombicosidodecahedron of edge length 1 has vertices given by:
 * $$\left(±\frac{5+\sqrt5}{4},\,0,\,±\frac{3+\sqrt5}{4}\right),$$
 * $$±\left(0,\,-\frac{3+\sqrt5}{4},\,\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,0\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac12,\,±\frac12\right),$$
 * $$±\left(±\frac12,\,-\frac{2+\sqrt5}{2},\,\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$±\left(±\frac{1+\sqrt5}{4},\,-\frac{1+\sqrt5}{2},\,\frac{3+\sqrt5}{4}\right).$$