- Compound of five stellated truncated cubes
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Compound of five stellated truncated cubes 
Type Uniform compound Index UC58 Polyhedra 5 stellated truncated cubes 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 cubes, 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))
- (±τ, ±(τ−1−τ−1√2), ±(2τ−1−τ√2))
- (±1, ±(τ−2+τ−1√2), ±(τ2−τ√2))
- (±(1−√2), ±(−τ−2+√2), ±(τ2−√2))
- (±(τ−τ√2), ±(−τ−1), ±(2τ−1−τ−1√2))
where τ = (1+√5)/2 is the golden ratio (sometimes written φ).
References
- Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society 79: 447–457, doi:10.1017/S0305004100052440, MR0397554.
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