# Small tetrisicositetrachoron

Small tetrisicositetrachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Suti |

Coxeter diagram | x3o4x3x4/3*a () |

Elements | |

Cells | 24 truncated octahedra, 24 quasitruncated hexahedra, 24 small rhombicuboctahedra, 24 quasitruncated cuboctahedra |

Faces | 192 triangles, 144+288 squares, 192 hexagons, 144 octagrams |

Edges | 288+576+576 |

Vertices | 576 |

Vertex figure | Isosceles trapezoidal pyramid, base edge lengths 1, √2, √2, √2; lateral edge lengths √3, √3, √2–√2, √2–√2 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Quith–8/3–quitco: 135° |

Toe–6–quitco: 120° | |

Sirco–3–quith: 120° | |

Sirco–4–quitco: 90° | |

Sirco–4–toe: 45° | |

Related polytopes | |

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

Regiment | Suti |

Conjugate | Great tetrisicositetrachoron |

Abstract & topological properties | |

Flag count | 18432 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}, order 1152 |

Convex | No |

Nature | Tame |

The **small tetrisicositetrachoron**, or **suti**, is a nonconvex uniform polychoron that consists of 24 truncated octahedra, 24 quasitruncated hexahedra, 24 small rhombicuboctahedra, and 24 quasitruncated cuboctahedra. 1 quasitruncated hexahedron, 1 truncated octahedron, 1 small rhombicuboctahedron, and 2 quasitruncated cuboctahedra join at each vertex.

The small tetrisicositetrachoron contains the vertices of a tesseractihexadecaquasitruncated prismatotesseractihexadecachoron.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a small tetrisicositetrachoron of edge length 1 are given by all permutations of:

The second set of vertices are identical to the vertices of an inscribed tesseractihexadecaquasitruncated prismatotesseractihexadecachoron.

## Related polychora[edit | edit source]

The small tetrisicositetrachoron is the colonel of a 3-member regiment that also includes the disicositetraquasitruncated disicositetrachoron and small rhombic trisicositetrachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 10: Prismatorhombates" (#409).

- Klitzing, Richard. "suti".