Small ditrigonal icosidodecahedron
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| Small ditrigonal icosidodecahedron | |
|---|---|
 | |
| Type | Uniform star polyhedron |
| Elements | F = 32, E = 60 V = 20 (χ = −8) |
| Faces by sides | 20{3}+12{5/2} |
| Wythoff symbol(s) | 3 | 5/2 3 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U30, C39, W70 |
| Bowers acronym | Sidtid |
 (3.5/2)3 (Vertex figure) |
 Small triambic icosahedron (dual polyhedron) |
In geometry, the small ditrigonal icosidodecahedron is a nonconvex uniform polyhedron, indexed as U30. It is constructed from Schwarz triangle (3 3 5/2) with Wythoff symbol 3 | 5/2 3, and Coxeter diagram 
. 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 (having the triangular faces in common), the ditrigonal dodecadodecahedron (having the pentagrammic 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 |
See also
External links
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