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.

Great rhombidodecahedron
TypeUniform star polyhedron
ElementsF = 42, E = 120
V = 60 (χ = 18)
Faces by sides30{4}+12{10/3}
Wythoff symbol
Symmetry groupIh, [5,3], *532
Index referencesU73, C89, W109
Dual polyhedronGreat rhombidodecacron
Vertex figure
4.10/3.4/3.10/7
Bowers acronymGird
3D model of a great rhombidodecahedron

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

Traditional filling

Modulo-2 filling


See also

References

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