Metabiaugmented truncated dodecahedron

The metabiaugmented truncated dodecahedron, or mabautid, is one of the 92 Johnson solids (J70). It consists of 2+2+2+2+2+4+4+4+4+4 triangles, 2+4+4 squares, 2 pentagons, and 2+2+2+4 decagons. It can be constructed by attaching two pentagonal cupolas to two non-opposite, non-adjacent decagonal faces of the truncated dodecahedron.

Vertex coordinates
A metabiaugmented truncated dodecahedron of edge length 1 has vertices given by all even permutations of: plus the following additional vertices:
 * $$\left(0,\,±\frac12,\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{15+13\sqrt5}{20},\,3\frac{5+\sqrt5}{10}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{25+13\sqrt5}{20},\,\frac{25+\sqrt5}{20}\right),$$
 * $$\left(0,\,±\frac{10+9\sqrt5}{10},\,\frac{15+\sqrt5}{20}\right).$$