Truncated great dodecahedron
Truncated great dodecahedron | |
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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 |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Truncated_great_dodecahedron.stl/220px-Truncated_great_dodecahedron.stl.png)
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}.
Related polyhedra
[edit]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 |
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Coxeter-Dynkin diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Picture | ![]() | ![]() | ![]() | ![]() | ![]() |
Small stellapentakis dodecahedron
[edit]Small stellapentakis dodecahedron | |
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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 |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/6/60/Small_stellapentakis_dodecahedron.stl/220px-Small_stellapentakis_dodecahedron.stl.png)
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
[edit]References
[edit]- ^ 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 links
[edit]- Weisstein, Eric W. "Truncated great dodecahedron". MathWorld.
- Weisstein, Eric W. "Small stellapentakis dodecahedron". MathWorld.
- Uniform polyhedra and duals
![](http://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Small_stellated_dodecahedron_truncations.gif/240px-Small_stellated_dodecahedron_truncations.gif)