Great rhombidodecahedron

Great rhombidodecahedron
TypeUniform star polyhedron
ElementsF = 42, E = 120
V = 60 (χ = 18)
Faces by sides30{4}+12{10/3}
Wythoff symbol2 5/3 (3/2 5/4) |
Symmetry groupIh, [5,3], *532
Index referencesU73, C89, W109
Dual polyhedronGreat rhombidodecacron
Vertex figure
4.10/3.4/3.10/7
Bowers acronymGird

In geometry, the great rhombidodecahedron is a nonconvex uniform polyhedron, indexed as U73. 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

Filling

There is some controversy on how to colour the faces of this polyhedron. Although the common way to fill in a polygon is to just colour its whole interior, this can result in some filled regions hanging as membranes over empty space. Hence, the "neo filling" is sometimes used instead as a more accurate filling. In the neo filling, orientable polyhedra are filled traditionally, but non-orientable polyhedra have their faces filled with the modulo-2 method (only odd-density regions are filled in).[1]


Traditional filling

"Neo filling"

See also

References

External links

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