# Augmented cube

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Augmented cube | |
---|---|

Rank | 3 |

Type | Isohedral |

Elements | |

Faces | 24 triangles |

Edges | 12+24 |

Vertices | 6+8 |

Vertex figure | 8 triambi, 6 squares |

Measures (edge length 1) | |

Circumradius | 8 (6-fold):
6 (4-fold): |

Volume | |

Number of external pieces | 24 |

Related polytopes | |

Dual | Semi-uniform hypertruncated octahedron |

Conjugate | Excavated cube |

Convex hull | Triakis octahedron |

Convex core | Semi-uniform-dual tetrakis cube |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | B_{3}, order 48 |

Convex | No |

Nature | Tame |

The **augmented cube** is an isohedral deltahedron. It can be formed by augmenting every face of the regular cube with a square pyramid. It is also a non-convex variant of the tetrakis cube.

An interesting property of this polyhedron is that its convex hull is the exact uniform dual triakis octahedron.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a cube of edge length 1, centered at the origin, are given by all sign changes and permutations of:

- ,
- .