Compound of five cuboctahedra

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Compound of five cuboctahedra
File:UC59-5 cuboctahedra.png
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)

In geometry, this uniform polyhedron compound is a composition of 5 cuboctahedra. It has icosahedral symmetry Ih. It could also be called the anticosicosahedron.

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).

Construction

The compound of 5 cuboctahedra could be made by the rectification of the compound of five cubes or compound of five octahedra. It could also be formed by the expansion of the compound of five or ten tetrahedra.

References

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