# Quasitruncated hexahedral prism

The **quasitruncated hexahedral prism** or **quithip**, is a prismatic uniform polychoron that consists of 2 quasitruncated hexahedra, 6 octagrammic prisms, and 8 triangular prisms. Each vertex joins 1 quasitruncated hexahedron, 1 octagrammic prism, and 2 triangular prisms. As the name suggests, it is a prism based on the quasitruncated hexahedron.

Quasitruncated hexahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Quithip |

Coxeter diagram | x x4/3x3o () |

Elements | |

Cells | 8 triangular prisms, 6 octagrammic prisms, 2 quasitruncated hexahedra |

Faces | 16 triangles, 12+24 squares, 12 octagrams |

Edges | 24+24+48 |

Vertices | 48 |

Vertex figure | Sphenoid, edge lengths 1, √2–√2, √2–√2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Stop–4–stop: 90° |

Quith–8/3–stop: 90° | |

Quith–3–trip: 90° | |

Trip–4–stop: | |

Height | 1 |

Central density | 7 |

Number of external pieces | 56 |

Related polytopes | |

Army | Semi-uniform Sircope |

Regiment | Quithip |

Dual | Great triakis octahedral tegum |

Conjugate | Truncated cubic prism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×A_{1}, order 96 |

Convex | No |

Nature | Tame |

The quasitruncated hexahedral prism can be vertex-inscribed into the sphenoverted tesseractitesseractihexadecachoron and the great distetracontoctachoron.

## Vertex coordinatesEdit

The vertices of a quasitruncated hexahedral prism of edge length 1 are given by all permutations of the first three coordinates of:

## External linksEdit

- Bowers, Jonathan. "Category 19: Prisms" (#905).

- Klitzing, Richard. "quithip".