Compound of five cuboctahedra

From Wikipedia, the free encyclopedia

Compound of five cuboctahedra
Type Uniform compound
Index UC59
Polyhedra 5 cuboctahedra
Faces 40 triangles, 30 squares
Edges 120
Vertices 60
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent pyritohedral (Th)

This uniform polyhedron compound is a composition of 5 cuboctahedra. It has icosahedral symmetry Ih.

[edit] Cartesian coordinates

Cartesian coordinates for the vertices of this compound are all the cyclic permutations of

(±2, 0, ±2)
(±τ, ±τ−1, ±(2τ−1))
(±1, ±τ−2, ±τ2)

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.
This polyhedron-related article is a stub. You can help Wikipedia by expanding it.
Languages