# Hemitesseractihemioctachoron

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Hemitesseractihemioctachoron | |
---|---|

Rank | 4 |

Type | Scaliform |

Notation | |

Bowers style acronym | Hatho |

Elements | |

Cells | 4 tetrahedra, 4 bowtie tegums |

Faces | 16 triangles, 4 squares |

Edges | 4+16 |

Vertices | 8 |

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

Measures (edge length 1) | |

Circumradius | |

Related polytopes | |

Army | Hex |

Regiment | Sub-regimental to hex |

Conjugate | None |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | K_{2}≀S_{2}, order 32 |

Convex | No |

Nature | Tame |

The **hemitesseractihemioctachoron**, or **hatho**, is a scaliform polychoron. It has 4 tetrahedra and 4 central bowtie tegums as cells, with 2 tetrahedra and 3 bowtie tegums at each vertex in the form of a bowtie pyramid. It can be obtained by chopping off two opposite quadrants of a tesseractihemioctachoron, or as a bowtie duotegum as the central tetrahedra degenerate into squares.

It is a faceting of the hexadecachoron, using all its vertices and a subset of its edges.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of the hexadecachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category S1: Simple Scaliforms" (#S8).

- Klitzing, Richard. "hatho".