# Great dodecicosahedron

Great dodecicosahedron
Type Uniform star polyhedron
Elements F = 32, E = 120
V = 60 (χ = −28)
Faces by sides 20{6}+12{10/3}
Wythoff symbol 3 5/3 (3/2 5/2) |
Symmetry group Ih, [5,3], *532
Index references U63, C79, W101
Dual polyhedron Great dodecicosacron
Vertex figure
6.10/3.6/5.10/7
Bowers acronym Giddy

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.[1] Its vertex figure is a crossed quadrilateral.

3D model of a great dodecicosahedron

It has a composite Wythoff symbol, 3 ​53 (​3252) |, requiring two different Schwarz triangles to generate it: (3 ​5332) and (3 ​5352). (3 ​5332 | represents the great dodecicosahedron with an extra 12 {​102} pentagons, and 3 ​5352 | represents it with an extra 20 {​62} triangles.)

Its vertex figure 6.​103.​65.​107 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).

 Truncated dodecahedron Great icosicosidodecahedron Great ditrigonal dodecicosidodecahedron Great dodecicosahedron