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Great rhombidodecahedron

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Great rhombidodecahedron
Type Uniform star polyhedron
Elements F = 42, E = 120
V = 60 (χ = −18)
Faces by sides 30{4}+12{10/3}
Coxeter diagram (with extra double-covered triangles)
(with extra double-covered pentagrams)
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.

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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
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Traditional filling

Modulo-2 filling


See also

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References

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  1. ^ Maeder, Roman. "73: great rhombidodecahedron". MathConsult.
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