Compound of five stellated truncated hexahedra

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Compound of five stellated truncated hexahedra
UC58-5 quasitruncated hexahedra.png
Type Uniform compound
IndexUC58
Polyhedra5 stellated truncated hexahedra
Faces40 triangles, 30 octagrams
Edges180
Vertices120
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

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