# Great ditrigonal icosidodecahedron

In geometry, the **great ditrigonal icosidodecahedron** (or **great ditrigonary icosidodecahedron**) is a nonconvex uniform polyhedron, indexed as U_{47}. It has 4 Schwarz triangle equivalent constructions, for example Wythoff symbol **3 | 3 5/4** gives Coxeter diagram *altered great stellated dodecahedron* or *converted great icosahedron*.

Great ditrigonal icosidodecahedron | |
---|---|

Type | Uniform star polyhedron |

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

Faces by sides | 20{3}+12{5} |

Wythoff symbol | ^{3}/_{2} | 3 53 | 3/2 5 3 | 3 5/4 3/2 | 3/2 5/4 |

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

Index references | U_{47}, C_{61}, W_{87} |

Dual polyhedron | Great triambic icosahedron |

Vertex figure | ((3.5) ^{3})/2 |

Bowers acronym | Gidtid |

Its circumradius is times the length of its edge,[1] a value it shares with the cube.

## Related polyhedra

Its convex hull is a regular dodecahedron. It additionally shares its edge arrangement with the small ditrigonal icosidodecahedron (having the triangular faces in common), the ditrigonal dodecadodecahedron (having the pentagonal faces in common), and the regular compound of five cubes.

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 |

## References

- Weisstein, Eric W (2003),
*CRC concise encyclopedia of mathematics*, Boca Raton: Chapman & Hall/CRC, ISBN 1-58488-347-2