# Prismatorhombated demitesseract

The **prismatorhombated demitesseract** is a convex semi-uniform polychoron that is a variant of the rectified icositetrachoron with demitesseractic symmetry. As such it can be represented by x3o3y *b3z, and has 24 rhombitetratetrahedra (of three types, forms x3o3y, x3o3z, and y3o3z) and 24 cuboids (type x y z) as cells, with 3 edge lengths.

Prismatorhombated demitesseract | |
---|---|

Rank | 4 |

Type | Semi-uniform |

Space | Spherical |

Notation | |

Coxeter diagram | x3o3y *b3z |

Elements | |

Cells | 24 cuboids, 8+8+8 rhombitetratetrahedra |

Faces | 32+32+32 triangles, 48+48+48 rectangles |

Edges | 96+96+96 |

Vertices | 96 |

Vertex figure | Skewed wedge |

Measures (edge lengths a, b, c) | |

Circumradius | |

Dichoral angles | Ratet–4–cuboid: 135° |

Ratet–3–ratet: 120° | |

Central density | 1 |

Related polytopes | |

Dual | Skewed notched enneacontihexachoron |

Conjugate | Prismatorhombated demitesseract |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | D4, order 192 |

Convex | Yes |

Nature | Tame |

## Vertex coordinatesEdit

A prismatorhombated demitesseract with edge lengths a, b, and c has vertices given by all permutations and even sign changes of: