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

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.

References

• Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457,
  MR 0397554
  .