Compound of five stellated truncated hexahedra

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

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), ±(φ^2−φ√2))

(±(1−√2), ±(−φ^−2+√2), ±(φ^2−√2))

(±(φ−φ√2), ±(−φ^−1), ±(2φ−1−φ^−1√2))

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.