Rhombidodecadodecahedron
From Wikipedia, the free encyclopedia
| Rhombidodecadodecahedron | |
|---|---|
 |
|
| Type | Uniform polyhedron |
| Elements | F = 54, E = 120 V = 60 (χ = -6) |
| Faces by sides | 30{4}+12{5}+12{5/2} |
| Wythoff symbol | 5/2 5 | 2 |
| Symmetry group | Ih |
| Index references | U38, C48, W76 |
 4.5/2.4.5 (Vertex figure) |
 Medial deltoidal hexecontahedron (dual polyhedron) |
In geometry, the rhombidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U38.
By the Wythoff construction this polyhedra can also be named a cantellated great dodecahedron.
It shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms.
[edit] Cartesian coordinates
Cartesian coordinates for the vertices of a uniform great rhombicosidodecahedron are all the even permutations of
- (±1/τ2, 0, ±τ2))
- (±1, ±1, ±(2τ−1))
- (±2, ±1/τ, ±τ)
where τ = (1+√5)/2 is the golden ratio (sometimes written φ).
