Compound of five stellated truncated hexahedra

This uniform polyhedron compound is a composition of 5 stellated truncated hexahedra, formed by star-truncating each of the cubes in the compound of 5 cubes.

Compound of five stellated truncated hexahedra
TypeUniform compound
IndexUC58
Polyhedra5 stellated truncated hexahedra
Faces40 triangles, 30 octagrams
Edges180
Vertices120
Symmetry groupicosahedral (Ih)
Subgroup restricting to one constituentpyritohedral (Th)

Cartesian coordinates

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

(±(2−2), ±2, ±(2−2))
(±φ, ±(φ−1−φ−12), ±(2φ−1−φ2))
(±1, ±(φ−2−12), ±(φ2−φ2))
(±(1−2), ±(−φ−2+2), ±(φ22))
(±(φ−φ2), ±(−φ−1), ±(2φ−1−φ−12))

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

References

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


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