| Truncated great dodecahedron | |
|---|---|
) | |
| 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 | ) 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&fras1;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.
) 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
| 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 |
)
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
- ^ 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
- Weisstein, Eric W. "Truncated great dodecahedron". MathWorld.
- Weisstein, Eric W. "Small stellapentakis dodecahedron". MathWorld.
- Uniform polyhedra and duals
)