# Antitruncated cube

Antitruncated cube | |
---|---|

Rank | 3 |

Type | Semi-uniform |

Elements | |

Faces | 8 triangles, 6 tetrapods |

Edges | 12+24 |

Vertices | 24 |

Vertex figure | Isosceles triangle, edge lengths 1, √2-√2, √2-√2 |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Sirco |

Dual | Antiapiculated octahedron |

Convex core | Cube |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | B3, order 48 |

Convex | No |

Nature | Tame |

The **antitruncated cube** or **inflected truncated cube** is a semi-uniform polyhedron. It has 8 triangles and 6 tetrapods as faces and an isosceles triangle as a vertex figure, having one triangle and two tetrapods meeting at each vertex. It is both the antitruncation (sometimes called inflected truncation) of the cube and a faceting of the small rhombicuboctahedron.

It is isomorphic to the truncated cube.

This polyhedron cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1: ≈ 1:1.41421) would yield an octahedron with three stellated squares instead.

## Vertex coordinates[edit | edit source]

The coordinates of the antitruncated cube are shared by that of the rhombicuboctahedron, being all permutations of:

## Variations[edit | edit source]

The antitruncated cube is part of a very similar teepee where the triangles are resized, but the distances between them stay the same.