Great rhombidodecahedron

Great rhombidodecahedron
Great rhombidodecahedron.png
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 Great rhombidodecahedron vertfig.png
4.10/3.4/3.10/7
Bowers acronym Gird

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.

3D model of a great rhombidodecahedron

Related polyhedraEdit

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

GalleryEdit

 
Traditional filling
 
Modulo-2 filling


See alsoEdit

ReferencesEdit

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

External linksEdit