Great ditrigonal icosidodecahedron
| Great ditrigonal icosidodecahedron | |
|---|---|
 | |
| Type | Uniform star polyhedron |
| Elements | F = 32, E = 60 V = 20 (χ = −8) |
| Faces by sides | 20{3}+12{5} |
| Wythoff symbol | 3/2 | 3 5 3 | 3/2 5 3 | 3 5/4 3/2 | 3/2 5/4 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U47, C61, W87 |
| Dual polyhedron | Great triambic icosahedron |
| Vertex figure |  ((3.5)3)/2 |
| Bowers acronym | Gidtid |
In geometry, the great ditrigonal icosidodecahedron is a nonconvex uniform polyhedron, indexed as U47. It has extended Schläfli symbol a{5/2,3} or c{3,5/2}, as an altered great stellated dodecahedron or converted great icosahedron, and Coxeter diagram 
. It has 4 Schwarz triangle equivalent constructions, for example Wythoff symbol 3 | 3/2 5, and Coxeter diagram 
.
Its circumradius is 
times the length of its edge,[1] a value it shares with the cube.
Related polyhedra
Its convex hull is a regular dodecahedron. It additionally shares its edge arrangement with the small ditrigonal icosidodecahedron (having the triangular faces in common), the ditrigonal dodecadodecahedron (having the pentagonal faces in common), and the regular compound of five cubes.
 Small ditrigonal icosidodecahedron |
Great ditrigonal icosidodecahedron |
 Ditrigonal dodecadodecahedron |
 Dodecahedron (convex hull) |
 Compound of five cubes |
References
- ↑ Weisstein, Eric W (2003), CRC concise encyclopedia of mathematics, Boca Raton: Chapman & Hall/CRC, ISBN 1-58488-347-2