# Tetrahedron atop truncated tetrahedron

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Tetrahedron atop truncated tetrahedron | |
---|---|

Rank | 4 |

Type | Segmentotope |

Notation | |

Bowers style acronym | Tetatut |

Coxeter diagram | xx3ox3oo&#x |

Elements | |

Cells | 1+4 tetrahedra, 4 triangular cupolas, 1 truncated tetrahedron |

Faces | 4+4+12 triangles, 6 squares, 4 hexagons |

Edges | 6+6+12+12 |

Vertices | 4+12 |

Vertex figures | 4 triangular prisms, edge lengths 1 (base) and √2 (sides) |

12 skewed triangular pyramids, edge lengths 1 (base) and √2, √3, √3 (sides) | |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Tet–3–tricu: 120° |

Tricu–4–tricu: 90° | |

Tet–3–tut: 60° | |

Tut-6-tricu: 60° | |

Height | |

Central density | 1 |

Related polytopes | |

Army | Tetatut |

Regiment | Tetatut |

Dual | Tetrahedral-triakis tetrahedral tegmoid |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}×I, order 24 |

Convex | Yes |

Nature | Tame |

**Tetrahedron atop truncated tetrahedron**, or **tetatut**, is a CRF segmentochoron (designated K-4.56 on Richard Klitzing's list). As the name suggests, it consists of a tetrahedron and a truncated tetrahedron as bases, connected by 4 further tetrahedra and 4 triangular cupolas.

It can be obtained as a segment of the rectified tesseract, which can be formed by attaching these segmentochora to both bases of the truncated tetrahedral cupoliprism.

## Vertex coordinates[edit | edit source]

The vertices of a tetrahedron atop truncated tetrahedronsegmentochoron of edge length 1 are given by:

- and all even sign changes of first three coordinates
- and all permutatoins and even sign changes of first three coordinates

## External links[edit | edit source]

- Klitzing, Richard. "tetatut".