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Compound of five truncated cubes

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Compound of five truncated cubes
Type Uniform compound
Index UC57
Polyhedra 5 truncated cubes
Faces 40 triangles, 30 octagons
Edges 180
Vertices 120
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.

Cartesian coordinates

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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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  • Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, Bibcode:1976MPCPS..79..447S, doi:10.1017/S0305004100052440, MR 0397554, S2CID 123279687.