# Truncated tesseractihemioctachoron

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Truncated tesseractihemioctachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Titho |

Coxeter diagram | (x3x3x3o3/2*a)/2 (/2) |

Elements | |

Cells | 8 tetrahemihexahedra, 8 truncated tetrahedra, 4 truncated octahedra |

Faces | 32 triangles, 24 squares, 32 hexagons |

Edges | 24+96 |

Vertices | 48 |

Vertex figure | Bowtie pyramid, base edge lengths 1 and √2, side edge length √3 |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Thah–3–tut: 120° |

Thah–4–toe: 90° | |

Tut–6–toe: 60° | |

Number of external pieces | 72 |

Level of complexity | 17 |

Related polytopes | |

Army | Thex |

Regiment | Thex |

Conjugate | None |

Abstract & topological properties | |

Flag count | 1536 |

Orientable | No |

Properties | |

Symmetry | D_{4}, order 192 |

Convex | No |

Nature | Tame |

The **truncated tesseractihemioctachoron**, or **titho**, is a nonconvex uniform polychoron that consists of 8 tetrahemihexahedra, 8 truncated tetrahedra, and 4 truncated octahedra. One tetrahemihexahedron, two truncated tetrahedra, and two truncated octahedra join at each vertex. As the name suggests, it can be obtained by truncating the tesseractihemioctachoron.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the truncated hexadecachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 2: Truncates" (#30).

- Klitzing, Richard. "titho".