# Quasitruncated tesseract

The **quasitruncated tesseract**, or **quitit**, is a nonconvex uniform polychoron that consists of 16 regular tetrahedra and 8 quasitruncated hexahedra. 1 tetrahedron and three quasitruncated hexahedra join at each vertex. As the name suggests, it can be obtained by quasitruncating the tesseract.

Quasitruncated tesseract | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Quitit |

Coxeter diagram | x4/3x3o3o () |

Elements | |

Cells | 16 tetrahedra, 8 quasitruncated hexahedra |

Faces | 64 triangles, 24 octagrams |

Edges | 32+96 |

Vertices | 64 |

Vertex figure | Triangular pyramid, edge lengths 1 (base) and √2–√2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Quith–8/3–quith: 90° |

Quith–3–tet: 60° | |

Central density | -1 |

Number of external pieces | 120 |

Level of complexity | 25 |

Related polytopes | |

Army | Sidpith, edge length |

Regiment | Quitit |

Conjugate | Truncated tesseract |

Convex core | Hexadecachoron |

Abstract & topological properties | |

Flag count | 1536 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{4}, order 384 |

Convex | No |

Nature | Tame |

## Vertex coordinates edit

The vertices of a quasitruncated tesseract of edge length 1 are given by all permutations of:

## Cross-sections edit

## External links edit

- Bowers, Jonathan. "Category 2: Truncates" (#34).

- Klitzing, Richard. "quitit".