# Small rhombated hexadecachoron

The **small rhombated hexadecachoron** is a convex semi-uniform polychoron that is a variant of the rectified icositetrachoron with tesseractic symmetry. As such it can be represented by o4y3o3x, and has 8 cuboctahedra of size y, 16 rhombitetratetrahedra of type x3o3y, and 24 square prisms of type x y4o as cells, with two edge lengths.

Small rhombated hexadecachoron | |
---|---|

Rank | 4 |

Type | Semi-uniform |

Notation | |

Coxeter diagram | o4y3o3x |

Elements | |

Cells | 24 square prisms, 8 cuboctahedra, 16 rhombitetratetrahedra |

Faces | 32+64 triangles, 48 squares, 96 rectangles |

Edges | 96+192 |

Vertices | 96 |

Vertex figure | Wedge |

Measures (edge lengths a (surrounding 2 rhombitetratetrahedra), b (of cuboctahedra)) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Co–4–squip: 135° |

Ratet–4–squip: 135° | |

Co–3–ratet: 120° | |

Ratet–3–ratet: 120° | |

Central density | 1 |

Related polytopes | |

Dual | Small notched enneacontihexachoron |

Conjugate | Small rhombated hexadecachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{4}, order 384 |

Convex | Yes |

Nature | Tame |

## Vertex coordinates edit

A small rhombated hexadecachoron with edge lengths a and b has vertices given by all permutations of:

- .