Truncated great dodecahedron

Truncated great dodecahedron
Great truncated dodecahedron.png
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 Truncated great dodecahedron vertfig.png
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.[1] It is given a Schläfli symbol t{5,​52}.

3D model of a truncated great dodecahedron

Related polyhedraEdit

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 dodecahedronEdit

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
 
3D model of a small stellapentakis 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.

See alsoEdit

ReferencesEdit

  1. ^ Maeder, Roman. "37: truncated great dodecahedron". MathConsult.

Wenninger, Magnus (1983), Dual Models, Cambridge University Press, doi:10.1017/CBO9780511569371, ISBN 978-0-521-54325-5, MR 0730208

External linksEdit

 
Animated truncation sequence from {​52, 5} to {5, ​52}