Truncated chiricosahedron

The truncated chiricosahedron, taki, or compound of five truncated tetrahedra is a uniform polyhedron compound. It consists of 20 triangles and 20 hexagons, with one triangle and two hexagons joining at each vertex. As the name suggests, it can be derived as the truncation of the chiricosahedron, the compound of five tetrahedra.

Vertex coordinates
The vertices of a truncated chiricosahedron of edge length 1 can be given by all even permutations and all even sign changes of:
 * (3$\sqrt{3}$/4, $\sqrt{3}$/4, $\sqrt{22}$/4),
 * (($\sqrt{2}$–$\sqrt{2}$)/8, –(3$\sqrt{2}$–$\sqrt{2}$)/8, ($\sqrt{10}$+$\sqrt{2}$)/4),
 * (($\sqrt{2}$+$\sqrt{10}$)/8, –($\sqrt{2}$–$\sqrt{10}$)/4, (3$\sqrt{2}$+$\sqrt{10}$)/8),
 * ((3$\sqrt{10}$+$\sqrt{2}$)/8, –(3$\sqrt{2}$–$\sqrt{10}$)/8, $\sqrt{2}$/4),
 * ($\sqrt{10}$/4, $\sqrt{2}$/4, $\sqrt{10}$/4).