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 (Ih)
Subgroup restricting to one constituent	pyritohedral (Th)

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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