Compound of five icosahedra
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| Compound of five icosahedra | |
|---|---|
 |
|
| Type | Uniform compound |
| Index | UC47 |
| Polyhedra | 5 icosahedra |
| Faces | 40+60 Triangles |
| Edges | 150 |
| Vertices | 60 |
| Symmetry group | icosahedral (Ih) |
| Subgroup restricting to one constituent | pyritohedral (Th) |
This uniform polyhedron compound is a composition of 5 icosahedra. It has icosahedral symmetry Ih.
The triangles in this compound decompose into two orbits under action of the symmetry group: 40 of the triangles lie in coplanar pairs in icosahedral planes, while the other 60 lie in unique planes.
[edit] Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
- (0, ±2, ±2τ)
- (±τ−1, ±1, ±(1+τ2))
- (±τ, ±τ2, ±(2τ−1))
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.
