# Small ditrigonal icosidodecahedron

In geometry, the **small ditrigonal icosidodecahedron** (or **small ditrigonary icosidodecahedron**) is a nonconvex uniform polyhedron, indexed as U_{30}. It has extended Schläfli symbol a{5,3}, as an *altered dodecahedron*, and Coxeter diagram

Small ditrigonal icosidodecahedron | |
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Type | Uniform star polyhedron |

Elements | F = 32, E = 60V = 20 (χ = −8) |

Faces by sides | 20{3}+12{^{5}/_{2}} |

Wythoff symbol | 3 | ^{5}/_{2} 3 |

Symmetry group | I_{h}, [5,3], *532 |

Index references | U_{30}, C_{39}, W_{70} |

Dual polyhedron | Small triambic icosahedron |

Vertex figure | (3. ^{5}/_{2})^{3} |

Bowers acronym | Sidtid |

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.

## 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. 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{5,3} | a{5/2,3} | b{5,5/2} |
---|---|---|

Small ditrigonal icosidodecahedron |
Great ditrigonal icosidodecahedron |
Ditrigonal dodecadodecahedron |

Dodecahedron (convex hull) |
Compound of five cubes |
Spherical compound of 5 cubes |