Great dodecicosahedron

Great dodecicosahedron
File:Great dodecicosahedron.png
Type	Uniform star polyhedron
Elements	F = 32, E = 120 V = 60 (χ = −28)
Faces by sides	20{6}+12{10/3}
Coxeter diagram	Template:CDD (with extra double-covered triangles) Template:CDD (with extra double-covered pentagons)
Wythoff symbol
Symmetry group	Ih, [5,3], *532
Index references	U63, C79, W101
Dual polyhedron	Great dodecicosacron
Vertex figure	File:Great dodecicosahedron vertfig.png 6.10/3.6/5.10/7
Bowers acronym	Giddy

File:Great dodecicosahedron.stl

3D model of a great dodecicosahedron

In geometry, the great dodecicosahedron (or great dodekicosahedron) is a nonconvex uniform polyhedron, indexed as U₆₃. It has 32 faces (20 hexagons and 12 decagrams), 120 edges, and 60 vertices. Its vertex figure is a crossed quadrilateral.

It has a composite Wythoff symbol, 3 5⁄3 (3⁄2 5⁄2) |, requiring two different Schwarz triangles to generate it: (3 5⁄3 3⁄2) and (3 5⁄3 5⁄2). (3 5⁄3 3⁄2 | represents the great dodecicosahedron with an extra 12 Template:Mset pentagons, and 3 5⁄3 5⁄2 | represents it with an extra 20 Template:Mset triangles.)

Its vertex figure 6.10⁄3.6⁄5.10⁄7 is also ambiguous, having two clockwise and two counterclockwise faces around each vertex.

Related polyhedra

It shares its vertex arrangement with the truncated dodecahedron. It additionally shares its edge arrangement with the great icosicosidodecahedron (having the hexagonal faces in common) and the great ditrigonal dodecicosidodecahedron (having the decagrammic faces in common).

File:Truncated dodecahedron.png Truncated dodecahedron

File:Great icosicosidodecahedron.png Great icosicosidodecahedron

File:Great ditrigonal dodecicosidodecahedron.png Great ditrigonal dodecicosidodecahedron

File:Great dodecicosahedron.png Great dodecicosahedron

Gallery

File:Great dodecicosahedron.png Traditional filling

File:Great dodecicosahedron 2.png Modulo-2 filling

See also

• List of uniform polyhedra