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.