# Small rhombic tesseractihexadecachoron

The **small rhombic tesseractihexadecachoron**, or **sirth**, is a nonconvex uniform polychoron that consists of 8 truncated octahedra, 16 cubohemioctahedra, and 24 cubes. 2 of each type of cell join at each vertex.

Small rhombic tesseractihexadecachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Sirth |

Elements | |

Cells | 24 cubes, 16 cubohemioctahedra, 8 truncated octahedra |

Faces | 48+96 squares, 64 hexagons |

Edges | 96+192 |

Vertices | 96 |

Vertex figure | Butterfly wedge, edge lengths √2 (bases and sides of outer triangles) and √3 (sides of inner triangles) |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Cho–4–cube: 135° |

Cho–6–toe: 60° | |

Toe–4–cube: 45° | |

Related polytopes | |

Army | Rico |

Regiment | Rico |

Conjugate | None |

Convex core | Tesseract |

Abstract & topological properties | |

Flag count | 3840 |

Euler characteristic | –32 |

Orientable | No |

Properties | |

Symmetry | B_{4}, order 384 |

Convex | No |

Nature | Tame |

## Vertex coordinates edit

The vertices are the same as those of the regiment colonel, the rectified icositetrachoron.

## External links edit

- Bowers, Jonathan. "Category 6: Sphenoverts" (#148).