Compound of five truncated cubes

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Compound of five truncated cubes
UC57-5 truncated cubes.png
Type Uniform compound
IndexUC57
Polyhedra5 truncated cubes
Faces40 triangles, 30 octagons
Edges180
Vertices120
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent pyritohedral (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), ±2, ±(2+2))
(±τ, ±(τ−1−12), ±(2τ−1+τ2))
(±1, ±(τ−2−τ−12), ±(τ22))
(±(1+2), ±(−τ−22), ±(τ2+2))
(±(τ+τ2), ±(−τ−1), ±(2τ−1+τ−12))

where τ = (1+5)/2 is the golden ratio (sometimes written φ).

References