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Great stellated truncated dodecahedron 
Summary
| Great stellated truncated dodecahedron | |
|---|---|
| |
| Type | Uniform star polyhedron |
| Elements | F = 32, E = 90 V = 60 (χ = 2) |
| Faces by sides | 20{3}+12{10/3} |
| Coxeter diagram |      
|
| Wythoff symbol | 2 3 | 5/3 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U66, C83, W104 |
| Dual polyhedron | Great triakis icosahedron |
| Vertex figure |  3.10/3.10/3 |
| Bowers acronym | Quit Gissid |
In geometry, the great stellated truncated dodecahedron (or quasitruncated great stellated dodecahedron or great stellatruncated dodecahedron) is a nonconvex uniform polyhedron, indexed as U66. It has 32 faces (20 triangles and 12 decagrams), 90 edges, and 60 vertices.[1] It is given a Schläfli symbol t0,1{5/3,3}.
Related polyhedra edit
It shares its vertex arrangement with three other uniform polyhedra: the small icosicosidodecahedron, the small ditrigonal dodecicosidodecahedron, and the small dodecicosahedron:
 Great stellated truncated dodecahedron |
 Small icosicosidodecahedron |
 Small ditrigonal dodecicosidodecahedron |
 Small dodecicosahedron |
Cartesian coordinates edit
Cartesian coordinates for the vertices of a great stellated truncated dodecahedron are all the even permutations of
![{\displaystyle {\begin{array}{crclc}{\Bigl (}&0,&\pm \,\varphi ,&\pm {\bigl [}2-{\frac {1}{\varphi }}{\bigr ]}&{\Bigr )}\\{\Bigl (}&\pm \,\varphi ,&\pm \,{\frac {1}{\varphi }},&\pm \,{\frac {2}{\varphi }}&{\Bigr )}\\{\Bigl (}&\pm \,{\frac {1}{\varphi ^{2}}},&\pm \,{\frac {1}{\varphi }},&\pm \,2&{\Bigr )}\end{array}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f61a6462c912d00bfe57e66f64e407d5608bb9da)
where is the golden ratio.
See also edit
References edit
- ^ Maeder, Roman. "66: great stellated truncated dodecahedron". MathConsult.
External links edit
- Weisstein, Eric W. "Great stellated truncated dodecahedron". MathWorld.