Compound of five truncated cubes

Compound of five truncated cubes
TypeUniform compound
IndexUC57
Polyhedra5 truncated cubes
Faces40 triangles, 30 octagons
Edges180
Vertices120
Symmetry 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.

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


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