Truncated great dodecahedron

Truncated great dodecahedron
Type	Uniform star polyhedron
Elements	F = 24, E = 90 V = 60 (χ = −6)
Faces by sides	12{5/2}+12{10}
Wythoff symbol(s)	2 5/2 | 5 2 5/3 | 5
Symmetry group	Ih, [5,3], *532
Index references	U37, C47, W75
Bowers acronym	Tigid
10.10.5/2 (Vertex figure)	Small stellapentakis dodecahedron (dual polyhedron)

In geometry, the truncated great dodecahedron is a nonconvex uniform polyhedron, indexed as U₃₇. It is given a Schläfli symbol t_0,1{5,5/2}.

Related polyhedra

It shares its vertex arrangement with three other uniform polyhedra: the nonconvex great rhombicosidodecahedron, the great dodecicosidodecahedron, and the great rhombidodecahedron; and with the uniform compounds of 6 or 12 pentagonal prisms.

Nonconvex great rhombicosidodecahedron	Great dodecicosidodecahedron	Great rhombidodecahedron
Truncated great dodecahedron	Compound of six pentagonal prisms	Compound of twelve pentagonal prisms

This polyhedron is the truncation of the great dodecahedron:

The truncated small stellated dodecahedron looks like a dodecahedron on the surface, but it has 24 faces, 12 pentagons from the truncated vertices and 12 overlapping as (truncated pentagrams).

Name	Small stellated dodecahedron	Truncated small stellated dodecahedron	Dodecadodecahedron	Truncated great dodecahedron	Great dodecahedron
Coxeter-Dynkin diagram
Picture

See also

• List of uniform polyhedra

External links

• Weisstein, Eric W., "Truncated great dodecahedron", MathWorld.
• Uniform polyhedra and duals