Small ditrigonal icosidodecahedron
| Small ditrigonal icosidodecahedron | |
|---|---|
| Type | Uniform star polyhedron |
| Elements | F = 32, E = 60 V = 20 (χ = −8) |
| Faces by sides | 20{3}+12{5/2} |
| Coxeter diagram | |
| Wythoff symbol | 3 | 5/2 3 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U30, C39, W70 |
| Dual polyhedron | Small triambic icosahedron |
| Vertex figure | (3.5/2)3 |
| Bowers acronym | Sidtid |
In geometry, the small ditrigonal icosidodecahedron (or small ditrigonary icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U30. It has 32 faces (20 triangles and 12 pentagrams), 60 edges, and 20 vertices. It has extended Schläfli symbol a{5,3}, as an altered dodecahedron, and Coxeter diagram or .
It is constructed from Schwarz triangle (3 3 5⁄2) with Wythoff symbol 3 | 5⁄2 3. Its hexagonal vertex figure alternates equilateral triangle and pentagram faces.