Compound of five truncated cubes

Compound of five truncated cubesTypeUniform compoundIndexUC57Polyhedra5 truncated cubesFaces40 triangles, 30 octagonsEdges180Vertices120Symmetry groupicosahedral (Ih)Subgroup restricting to one constituentpyritohedral (Th) This uniform polyhedron compound is a composition of 5 truncated cubes, formed by truncating each of the cubes in the compound of 5 cubes. It is also called the truncated rhombihedron.

Cartesian coordinates Cartesian coordinates for the vertices of this compound are all the cyclic permutations of

(±(2+), ±, ±(2+)) (±τ, ±(τ−1+τ−1), ±(2τ−1+τ)) (±1, ±(τ−2−τ−1), ±(τ2+τ)) (±(1+), ±(−τ−2−), ±(τ2+)) (±(τ+τ), ±(−τ−1), ±(2τ−1+τ−1))

where τ = (1+)/2 is the golden ratio (sometimes written φ).

References .