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.

[edit] 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−2−1√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).

[edit] References

  • John Skilling, Uniform Compounds of Uniform Polyhedra, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 79, pp. 447-457, 1976.
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