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Small ditrigonal icosidodecahedron
Polyhedron with 32 faces / From Wikipedia, the free encyclopedia
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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.[1] It has extended Schläfli symbol a{5,3}, as an altered dodecahedron, and Coxeter diagram or
.
Small ditrigonal icosidodecahedron | |
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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 |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/3/39/Small_ditrigonal_icosidodecahedron.stl/640px-Small_ditrigonal_icosidodecahedron.stl.png)
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.