Great ditrigonal icosidodecahedron
In geometry, the great ditrigonal icosidodecahedron is a nonconvex uniform polyhedron, indexed as U47. It has 32 faces, 60 edges, and 20 vertices. It has 4 Schwarz triangle equivalent constructions, for example Wythoff symbol 3 | 3 gives Coxeter diagram =. It has extended Schläfli symbol a or c, as an altered great stellated dodecahedron or converted great icosahedron.
Its circumradius is times the length of its edge, 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, the ditrigonal dodecadodecahedron, and the regular compound of five cubes.| a | a | b |
| = | = | |
Small ditrigonal icosidodecahedron | Great ditrigonal icosidodecahedron | Ditrigonal dodecadodecahedron |
Dodecahedron | Compound of five cubes | - |