| Small stellated truncated dodecahedron | |
|---|---|
| Type | Uniform star polyhedron |
| Elements | F = 24, E = 90V = 60 (χ = −6) |
| Faces by sides | 12{5}+12{10/3} |
| Coxeter diagram | |
| Wythoff symbol | 2 5 | 5/32 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 |
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. It is given a Schläfli symbol t{5⁄3,5}, and Coxeter diagram .
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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
External links
References
Maeder, Roman. "58: small stellated truncated dodecahedron". MathConsult. https://www.mathconsult.ch/static/unipoly/58.html ↩