Great rhombidodecahedron

Great rhombidodecahedron
File:Great rhombidodecahedron.png
Type	Uniform star polyhedron
Elements	F = 42, E = 120 V = 60 (χ = −18)
Faces by sides	30{4}+12{10/3}
Coxeter diagram	Template:CDD (with extra double-covered triangles) Template:CDD (with extra double-covered pentagrams)
Wythoff symbol
Symmetry group	I_h, [5,3], *532
Index references	U₇₃, C₈₉, W₁₀₉
Dual polyhedron	Great rhombidodecacron
Vertex figure	File:Great rhombidodecahedron vertfig.png 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.

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).

File:Uniform great rhombicosidodecahedron.png Nonconvex great rhombicosidodecahedron	File:Great dodecicosidodecahedron.png Great dodecicosidodecahedron	File:Great rhombidodecahedron.png Great rhombidodecahedron
File:Great truncated dodecahedron.png Truncated great dodecahedron	File:UC34-6 pentagonal prisms.png Compound of six pentagonal prisms	File:UC35-12 pentagonal prisms.png Compound of twelve pentagonal prisms

File:Great rhombidodecahedron.png Traditional filling	File:Great rhombidodecahedron 2.png Modulo-2 filling