# Antitruncated great dodecahedron

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Antitruncated great dodecahedron | |
---|---|

Rank | 3 |

Type | Semi-uniform |

Elements | |

Faces | 12 pentagrams, 12 pentapods. |

Edges | 60+30 |

Vertices | 60 |

Related polytopes | |

Army | Srid |

Dual | Antiapiculated small stellated dodecahedron |

Convex core | Dodecahedron |

Abstract & topological properties | |

Euler characteristic | -6 |

Orientable | Yes |

Genus | 4 |

Properties | |

Convex | No |

Nature | Tame |

The **antitruncated great dodecahedron** or **inflected truncated great dodecahedron** is a semi-uniform polyhedron. It is both the antitruncation of the great dodecahedron and a faceting of the small rhombicosidodecahedron. It consists of 12 pentapods and 12 pentagrams, with an isosceles triangle vertex figure and 1 pentagram and 2 pentapods at a vertex.

## Vertex coordinates[edit | edit source]

The coordinates of the antitruncated great dodecahedron are the same as the small rhombicosidodecahedron, being

all permutations of

along with all even permutations of

## Variations[edit | edit source]

The antitruncated great dodecahedron is part of a teepee where the great dodecahedron is antitruncated by a different amount.