| Great rhombidodecahedron | |
|---|---|
) | |
| Type | Uniform star polyhedron |
| Elements | F = 42, E = 120 V = 60 (χ = −18) |
| Faces by sides | 30{4}+12{10/3} |
| Wythoff symbol | 2 5/3 (3/2 5/4) | |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U73, C89, W109 |
| Dual polyhedron | Great rhombidodecacron |
| Vertex figure | ) 4.10/3.4/3.10/7 |
| Bowers acronym | Gird |
)
3D model of a great rhombidodecahedron
In geometry, the great rhombidodecahedron is a nonconvex uniform polyhedron, indexed as U73. It has 42 faces (30 squares, 12 decagrams), 120 edges and 60 vertices.[1] Its vertex figure is a crossed quadrilateral.
Related polyhedra
It shares its vertex arrangement with the truncated great dodecahedron and the uniform compounds of 6 or 12 pentagonal prisms. It additionally shares its edge arrangement with the nonconvex great rhombicosidodecahedron (having the square faces in common), and with the great dodecicosidodecahedron (having the decagrammic faces in common).
) Nonconvex great rhombicosidodecahedron | ) Great dodecicosidodecahedron | ) Great rhombidodecahedron |
) Truncated great dodecahedron | ) Compound of six pentagonal prisms | ) Compound of twelve pentagonal prisms |
Gallery
) Traditional filling | ) Modulo-2 filling |
See also
References
- ^ Maeder, Roman. "73: great rhombidodecahedron". MathConsult.