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Truncated great dodecahedron

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Truncated great dodecahedron
Type Uniform star polyhedron
Elements F = 24, E = 90
V = 60 (χ = −6)
Faces by sides 12{5/2}+12{10}
Coxeter diagram
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
3D model of a truncated great dodecahedron

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{5,5/2}.

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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

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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 also

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References

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  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

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