Nonconvex great rhombicosidodecahedron
| Nonconvex great rhombicosidodecahedron | |
|---|---|
 | |
| Type | Uniform star polyhedron |
| Elements | F = 62, E = 120 V = 60 (χ = 2) |
| Faces by sides | 20{3}+30{4}+12{5/2} |
| Wythoff symbol(s) | 5/3 3 | 2 5/2 3/2 | 2 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U67, C84, W105 |
| Bowers acronym | Qrid |
 3.4.5/3.4 (Vertex figure) |
 Great deltoidal hexecontahedron (dual polyhedron) |
In geometry, the nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U67. It is also called the quasirhombicosidodecahedron. It is given a Schläfli symbol t0,2{5/3,3}. Its vertex figure is a crossed quadrilateral.
This model shares the name with the convex great rhombicosidodecahedron, also known as the truncated icosidodecahedron.
Cartesian coordinates
Cartesian coordinates for the vertices of a nonconvex 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).
Related polyhedra
It shares its vertex arrangement with the truncated great dodecahedron, and with the uniform compounds of 6 or 12 pentagonal prisms. It additionally shares its edge arrangement with the great dodecicosidodecahedron (having the triangular and pentagrammic faces in common), and the great rhombidodecahedron (having the square faces in common).
| Nonconvex great rhombicosidodecahedron |
 Great dodecicosidodecahedron |
 Great rhombidodecahedron |
 Truncated great dodecahedron |
 Compound of six pentagonal prisms |
 Compound of twelve pentagonal prisms |
See also
External links
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