Great dodecicosidodecahedron

Great dodecicosidodecahedron
File:Great dodecicosidodecahedron.png
Type	Uniform star polyhedron
Elements	F = 44, E = 120 V = 60 (χ = −16)
Faces by sides	20{3}+12{5/2}+12{10/3}
Coxeter diagram	Template:CDD
Wythoff symbol	5/3 5/3 3/2 \| 5/3
Symmetry group	I_h, [5,3], *532
Index references	U₆₁, C₇₇, W₉₉
Dual polyhedron	Great dodecacronic hexecontahedron
Vertex figure	File:Great dodecicosidodecahedron vertfig.png 3.10/3.5/2.10/7
Bowers acronym	Gaddid

3D model of a great dodecicosidodecahedron.

In geometry, the great dodecicosidodecahedron (or great dodekicosidodecahedron) is a nonconvex uniform polyhedron, indexed as U₆₁. It has 44 faces (20 triangles, 12 pentagrams and 12 decagrams), 120 edges and 60 vertices.^[1]

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 triangular and pentagrammic faces in common), and with the great rhombidodecahedron (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