# Antitruncated icosahedron

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Antitruncated icosahedron | |
---|---|

Rank | 3 |

Elements | |

Faces | 12 triangles, 20 tripods |

Edges | 60+30 |

Vertices | 60 |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Srid |

Dual | Antiapiculated dodecahedron |

Convex core | Icosahedron |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Convex | No |

Nature | Tame |

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

## Vertex coordinates[edit | edit source]

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

along with all even permutations of

## Variations[edit | edit source]

Continuing to antitruncate the icosahedron without letting vertices cross will form a teepee.