Great rhombidodecahedron
Polyhedron with 42 faces
Great rhombidodecahedron | |
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![]() | |
Type | Uniform star polyhedron |
Elements | F = 42, E = 120 V = 60 (χ = −18) |
Faces by sides | 30{4}+12{10/3} |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/3/30/Great_rhombidodecahedron.stl/220px-Great_rhombidodecahedron.stl.png)
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.
External links
- Weisstein, Eric W. "Great rhombidodecahedron". MathWorld.
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