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Compound of five truncated cubes

Polyhedral compound From Wikipedia, the free encyclopedia

Compound of five truncated cubes
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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.

Compound of five truncated cubes
Thumb
TypeUniform compound
IndexUC57
Polyhedra5 truncated cubes
Faces40 triangles, 30 octagons
Edges180
Vertices120
Symmetry groupicosahedral (Ih)
Subgroup restricting to one constituentpyritohedral (Th)
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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

  • 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.
  • McCooey, Robert. "Uniform Polyhedron Compounds". Hedron Dude. Retrieved 24 June 2025.


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