Antitruncated dodecahedron

The antitruncated dodecahedron or inflected truncated octahedron is a semi-uniform polyhedron. It consists of 20 triangles and 12 pentapods, and has 1 triangle and 2 pentapods at a vertex. It has an isosceles triangle as a vertex figure. It is the antitruncation of the dodecahedron and also a faceting of the small rhombicosidodecahedron.

Vertex coordinates
The antitruncated dodecahedron shares its vertices with the small rhombicosidodecahedron, being all permutations of


 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac12,\,±\frac12\right),$$

along with all even permutations of


 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right).$$

Variations
The antitruncated dodecahedron is part of a teepee where you continue to antitruncate the dodecahedron without the vertices crossing.