Great ditrigonal icosidodecahedron
From Wikipedia, the free encyclopedia
| Great ditrigonal icosidodecahedron | |
|---|---|
 |
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| Type | Uniform polyhedron |
| Elements | F = 32, E = 60 V = 20 (χ = -8) |
| Faces by sides | 20{3}+12{5} |
| Wythoff symbol | 3/2 | 3 5 |
| Symmetry group | Ih |
| Index references | U47, C61, W87 |
 ((3.5)3)/2 (Vertex figure) |
 Great triambic icosahedron (dual polyhedron) |
In geometry, the great ditrigonal icosidodecahedron is a nonconvex uniform polyhedron, indexed as U47.
The Great ditrigonal icosidodecahedron has 20 vertices, 60 edges, and 32 faces (20{3}+12{5}). The vertex configuration is ((3.5)3)/2. Its symmetry group is Ih, its Wythoff symbol is 3/2 | 3 5, and its Euler characteristic is χ=-8.
Its uniform index number is U47, its Kaleido index is K52, its number in Wenninger's Polyhedron Models is 87, and it was given the number 61 in Coxeter's 1954 paper, which first gave the complete list of the uniform polyhedra.
It shares the vertex arrangement with the regular dodecahedron. It additionally shares its edge arrangement with the small ditrigonal icosidodecahedron, the ditrigonal dodecadodecahedron, and the regular compound of five cubes.
