Compound of five cuboctahedraTypeUniform compoundIndexUC59Polyhedra5 cuboctahedraFaces40 triangles, 30 squaresEdges120Vertices60Symmetry groupicosahedral (Ih)Subgroup restricting to one constituentpyritohedral (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+)/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 .