Metabidiminished icosahedron

The metabidiminished icosahedron is one of the 92 Johnson solids (J62). It consists of 2+2+2+4 triangles and 2 pentagons. It can be constructed by removing two non-opposite, non-adjacent vertices from a regular icosahedron.

Vertex coordinates
A metabidiminished icosahedron of edge length 1 has the following vertices:


 * $$\left(±\frac{1+\sqrt5}{4},\,+\frac12,\,0\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(\frac12,\,0,\,±\frac{1+\sqrt5}{4}\right).$$