# Small rhombic trisicositetrachoron

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Small rhombic trisicositetrachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Sirti |

Elements | |

Cells | 24 small rhombihexahedra, 24 quasitruncated cuboctahedra, 24 cuboctatruncated cuboctahedra |

Faces | 288 squares, 192 hexagons, 144 octagons, 144 octagrams |

Edges | 288+576+576 |

Vertices | 576 |

Vertex figure | Butterfly pyramid, base edge lengths √2, √2+√2, √2, √2+√2; lateral edge lengths √3, √3, √2–√2, √2–√2 |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Sroh–8–cotco: 135° |

Sroh–4–quitco: 90° | |

Cotco–8/3–quitco: 90° | |

Cotco–6–quitco: 60° | |

Related polytopes | |

Army | Semi-uniform Prico, edge lengths (small rhombicuboctahedra), (sides of triangular prisms) |

Regiment | Suti |

Conjugate | Great rhombic trisicositetrachoron |

Abstract & topological properties | |

Flag count | 18432 |

Euler characteristic | –168 |

Orientable | No |

Properties | |

Symmetry | F_{4}, order 1152 |

Convex | No |

Nature | Tame |

The **small rhombic trisicositetrachoron**, or **sirti**, is a nonconvex uniform polychoron that consists of 24 small rhombihexahedra, 24 quasitruncated cuboctahedra, and 24 cuboctatruncated cuboctahedra. One small rhombihexahedron, two quasitruncated cuboctahedra, and two cuboctatruncated cuboctahedra join at each vertex.

It can be constructed as a blend of three tesseractihexadecaquasitruncated prismatotesseractihexadecachora. In the process the truncated octahedra blend out, while the octagonal prisms blend into small rhombihexahedra.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the small tetrisicositetrachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 10: Prismatorhombates" (#411).