Small stellated truncated dodecahedron
In geometry, the small stellated truncated dodecahedron (or quasitruncated small stellated dodecahedron or small stellatruncated dodecahedron) is a nonconvex uniform polyhedron, indexed as U58. It has 24 faces (12 pentagons and 12 decagrams), 90 edges, and 60 vertices.[1] It is given a Schläfli symbol t{5⁄3,5}, and Coxeter diagram 
.
| Small stellated truncated dodecahedron | |
|---|---|
 | |
| Type | Uniform star polyhedron |
| Elements | F = 24, E = 90 V = 60 (χ = −6) |
| Faces by sides | 12{5}+12{10/3} |
| Coxeter diagram |   |
| Wythoff symbol | 2 5 | 5/3 2 5/4 | 5/3 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U58, C74, W97 |
| Dual polyhedron | Great pentakis dodecahedron |
| Vertex figure |  5.10/3.10/3 |
| Bowers acronym | Quit Sissid |
3D model of a small stellated truncated dodecahedron
Related polyhedra
It shares its vertex arrangement with three other uniform polyhedra: the convex rhombicosidodecahedron, the small dodecicosidodecahedron and the small rhombidodecahedron.
It also has the same vertex arrangement as the uniform compounds of 6 or 12 pentagrammic prisms.
 Rhombicosidodecahedron |
 Small dodecicosidodecahedron |
 Small rhombidodecahedron |
Small stellated truncated dodecahedron |
 Compound of six pentagrammic prisms |
 Compound of twelve pentagrammic prisms |
See also
References
- Maeder, Roman. "58: small stellated truncated dodecahedron". MathConsult.
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