Truncated great dodecahedron

Truncated great dodecahedron
TypeUniform star polyhedron
ElementsF = 24, E = 90
V = 60 (χ = −6)
Faces by sides12{5/2}+12{10}
Wythoff symbol2 5/2 | 5
2 5/3 | 5
Symmetry groupIh, [5,3], *532
Index referencesU37, C47, W75
Dual polyhedronSmall stellapentakis dodecahedron
Vertex figure
10.10.5/2
Bowers acronymTigid

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

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
Animated truncation sequence from {5/2, 5} to {5, 5/2}

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
TypeStar polyhedron
Face
ElementsF = 60, E = 90
V = 24 (χ = −6)
Symmetry groupIh, [5,3], *532
Index referencesDU37
dual polyhedronTruncated great dodecahedron

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

See also

References

  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, doi:10.1017/CBO9780511569371, ISBN 978-0-521-54325-5, MR 0730208
  • Weisstein, Eric W. "Truncated great dodecahedron". MathWorld.
  • Weisstein, Eric W. "Small stellapentakis dodecahedron". MathWorld.
  • Uniform polyhedra and duals


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.