Uniform great rhombicosidodecahedron
From Wikipedia, the free encyclopedia
| Uniform great rhombicosidodecahedron | |
|---|---|
 |
|
| Type | Uniform polyhedron |
| Elements | F = 62, E = 120 V = 60 (χ = 2) |
| Faces by sides | 20{3}+30{4}+12{5/2} |
| Wythoff symbol | 5/33 | 2 |
| Symmetry group | Ih |
| Index references | U67, C84, W105 |
 3.4.5/3.4 (Vertex figure) |
 Great deltoidal hexecontahedron (dual polyhedron) |
In geometry, the uniform great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U67. It is also called the quasirhombicosidodecahedron.
This model shares the name with the convex great rhombicosidodecahedron, which is also called the truncated icosidodecahedron. Because of this confusion the word uniform was added to this article name.
It shares its vertex arrangement with the truncated great dodecahedron, and with the uniform compounds of 6 or 12 pentagonal prisms.
[edit] Cartesian coordinates
Cartesian coordinates for the vertices of a uniform great rhombicosidodecahedron are all the even permutations of
- (±1/τ2, 0, ±(2−1/τ))
- (±1, ±1/τ3, ±1)
- (±1/τ, ±1/τ2, ±2/τ)
where τ = (1+√5)/2 is the golden ratio (sometimes written φ).
