# Antitruncated dodecahedron

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

Rank | 3 |

Type | Semi-uniform |

Elements | |

Faces | 20 triangles, 12 pentapods |

Edges | 60+30 |

Vertices | 60 |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Srid |

Dual | Antiapiculated icosahedron |

Convex core | Dodecahedron |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Convex | No |

Nature | Tame |

The **antitruncated dodecahedron** or **inflected truncated dodecahedron** is a semi-uniform polyhedron. It consists of 20 triangles and 12 pentapods, and has 1 triangle and 2 pentapods at a vertex. It has an isosceles triangle as a vertex figure. It is the antitruncation of the dodecahedron and also a faceting of the small rhombicosidodecahedron.

## Vertex coordinates[edit | edit source]

The antitruncated dodecahedron shares its vertices with the small rhombicosidodecahedron, being all permutations of

along with all even permutations of

## Variations[edit | edit source]

The antitruncated dodecahedron is part of a teepee where you continue to antitruncate the dodecahedron without the vertices crossing.