# Antitruncated tetrahedron

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Antitruncated tetrahedron | |
---|---|

Rank | 3 |

Space | Spherical |

Elements | |

Faces | 4 triangles, 4 propeller tripods |

Edges | 12+6 |

Vertices | 12 |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Semiuniform ratet |

Dual | Antiapiculated tetrahedron |

Convex core | Tetrahedron |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Nature | Tame |

The **antitruncated tetrahedron** or **inflected truncated tetrahedron** is a semi-uniform polyhedron. It consists of 4 triangles and 4 propeller tripods. It has 1 triangle and 2 propeller tripods at a vertex, and an isosceles triangle vertex figure. It is the antitruncation of the tetrahedron and a faceting of a nonuniform rhombitetratetrahedron.

## Variations[edit | edit source]

Adjusting the size of the triangles in an antitruncated tetrahedron but keeping the distance between them forms a teepee.

## Related polyhedra[edit | edit source]

The antitruncated tetrahedron is topologically equivalent to the truncated tetrahedron