Compound of five stellated truncated hexahedra explained

bgcolor=#e7dcc3 colspan=2	Compound of five stellated truncated hexahedra
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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−))

(±φ, ±(φ⁻¹−φ⁻¹), ±(2φ−1−φ))

(±1, ±(φ⁻²+φ⁻¹), ±(φ²−φ))

(±(1−), ±(−φ⁻²+), ±(φ²−))

(±(φ−φ), ±(−φ⁻¹), ±(2φ−1−φ⁻¹))

where φ = (1+)/2 is the golden ratio.

References

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