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

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

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⁻¹√2), ±(2φ−1−φ√2))

(±1, ±(φ⁻²+φ⁻¹√2), ±(φ²−φ√2))

(±(1−√2), ±(−φ⁻²+√2), ±(φ²−√2))

(±(φ−φ√2), ±(−φ⁻¹), ±(2φ−1−φ⁻¹√2))

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

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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