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Compound of five stellated truncated hexahedra

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Compound of five stellated truncated hexahedra
Type Uniform compound
Index UC58
Polyhedra 5 stellated truncated hexahedra
Faces 40 triangles, 30 octagrams
Edges 180
Vertices 120
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent pyritohedral (Th)

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.

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))
(±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

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  • 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.