Compound of five cuboctahedra
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Short description: Polyhedral compound
| Compound of five cuboctahedra | |
|---|---|
| 200px | |
| 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
- Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society 79 (3): 447–457, doi:10.1017/S0305004100052440.
- McCooey, Robert. "Uniform Polyhedron Compounds". http://www.polytope.net/hedrondude/fivers.htm.
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