# 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 2 5/2 | 5
2 5/3 | 5
Symmetry group Ih, [5,3], *532
Index references U37, C47, W75
Dual polyhedron Small stellapentakis dodecahedron
Vertex figure 10.10.5/2
Bowers acronym Tigid

In geometry, the truncated great dodecahedron is a nonconvex uniform polyhedron, indexed as U37. It has 24 faces (12 pentagrams and 12 decagons), 90 edges, and 60 vertices. It is given a Schläfli symbol t{5,​52}.

## 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

### Small stellapentakis dodecahedron

Small stellapentakis dodecahedron

Type Star polyhedron
Face
Elements F = 60, E = 90
V = 24 (χ = −6)
Symmetry group Ih, [5,3], *532
Index references DU37
dual polyhedron Truncated great dodecahedron

The small stellapentakis dodecahedron (or small astropentakis dodecahedron) is a nonconvex isohedral polyhedron. It is the dual of the truncated great dodecahedron. It has 60 intersecting triangular faces.