Antitruncated icosahedron

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

Vertex coordinates
The antitruncated icosahedron shares its vertices with the small rhombicosidodecahedron, being all permutations of along with all even permutations of
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right).$$

Variations
Continuing to antitruncate the icosahedron without letting vertices cross will form a teepee.