Truncated great dodecahedron
| Truncated great dodecahedron | |
|---|---|
| File: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} |
| Coxeter diagram | Template:CDD |
| Wythoff symbol | 5 2 5/3 | 5 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U37, C47, W75 |
| Dual polyhedron | Small stellapentakis dodecahedron |
| Vertex figure | File: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{5,5/2}.
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.
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).
Small stellapentakis dodecahedron
Template:Uniform dual polyhedron stat table
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
References
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External links
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- Uniform polyhedra and duals
Template:Nonconvex polyhedron navigator
- ↑ Script error: No such module "citation/CS1".