Small ditrigonal icosidodecahedron
In geometry, the small ditrigonal icosidodecahedron is a nonconvex uniform polyhedron, indexed as U30. It has 32 faces, 60 edges, and 20 vertices. It has extended Schläfli symbol a, as an altered dodecahedron, and Coxeter diagram or.
It is constructed from Schwarz triangle with Wythoff symbol 3 | 3. Its hexagonal vertex figure alternates equilateral triangle and pentagram faces.
Related polyhedra
Its convex hull is a regular dodecahedron. It additionally shares its edge arrangement with the great ditrigonal icosidodecahedron, the ditrigonal dodecadodecahedron, and the regular compound of five cubes. As a simple polyhedron, it is also a hexakis truncated icosahedron where the triangles touching the pentagons are made coplanar, making the others concave.| a | a | b |
| = | = | |
Small ditrigonal icosidodecahedron | Great ditrigonal icosidodecahedron | Ditrigonal dodecadodecahedron |
Dodecahedron | Compound of five cubes | Spherical compound of 5 cubes |