# Augmented truncated tetrahedron

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Augmented truncated tetrahedron | |
---|---|

Rank | 3 |

Type | CRF |

Notation | |

Bowers style acronym | Autut |

Coxeter diagram | xxoo3oxux&#xt |

Elements | |

Faces | |

Edges | 3+3+3+3+3+6+6 |

Vertices | 3+3+3+6 |

Vertex figures | 3 rectangle, edge length 1 and √2 |

6 irregular tetragons, edge length 1, √2, 1, √3 | |

3+3 isosceles triangles, edge lengths 1, √3, √3 | |

Measures (edge length 1) | |

Volume | |

Dihedral angles | 3–4 join: |

3–6 join: | |

3–4 cupolaic: | |

3–6 tut: | |

6–6: | |

Central density | 1 |

Number of external pieces | 14 |

Level of complexity | 18 |

Related polytopes | |

Army | Autut |

Regiment | Autut |

Dual | Rhombirhombistellated triakis tetrahedron |

Conjugate | Augmented truncated tetrahedron |

Abstract & topological properties | |

Flag count | 108 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | A_{2}×I, order 6 |

Flag orbits | 18 |

Convex | Yes |

Nature | Tame |

The **augmented truncated tetrahedron** (OBSA: **autut**) is one of the 92 Johnson solids (J_{65}). It consists of 1+1+3+3 triangles, 3 squares, and 3 hexagons. It can be constructed by attaching a triangular cupola to one of the hexagonal faces of the truncated tetrahedron.

## Vertex coordinates[edit | edit source]

An augmented truncated tetrahedron of edge length 1 has vertices given by all even sign changes of:

- ,

plus all permutations of:

- .

## External links[edit | edit source]

- Klitzing, Richard. "autut".
- Quickfur. "The Augmented Truncated Tetrahedron".

- Wikipedia contributors. "Augmented truncated tetrahedron".
- McCooey, David. "Augmented Truncated Tetrahedron"