# Small hexadecafaceted prismatotesseractioctachoron

Small hexadecafaceted prismatotesseractioctachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Shafipto |

Coxeter diagram | |

Elements | |

Cells | 32 triangular prisms, 8 cubes, 8 small rhombicuboctahedra |

Faces | 64 triangles, 48+96 squares |

Edges | 96+96 |

Vertices | 64 |

Vertex figure | Irregular triangular hemiantipodium, edge lengths √2 (top triangle and sides) and 1 (base pseudo-triangle) |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Sirco–4–cube: 90° |

Sirco–3–trip: 90° | |

Sirco–4–trip: | |

Number of external pieces | 248 |

Level of complexity | 23 |

Related polytopes | |

Army | Sidpith |

Regiment | Sidpith |

Conjugate | Great hexadecafaceted prismatotesseractioctachoron |

Abstract & topological properties | |

Euler characteristic | 32 |

Orientable | No |

Properties | |

Symmetry | B_{4}, order 384 |

Convex | No |

Nature | Tame |

The **small hexadecafaceted prismatotesseractioctachoron**, or **shafipto**, is a nonconvex uniform polychoron that consists of 8 cubes, 32 triangular prisms, and 8 small rhombicuboctahedra. One cube, three triangular prisms, and three small rhombicuboctahedra join at each vertex.

It also has 16 tetrahedra and 24 cubes as pseudofacets.

It can be constructed as a blend of four small rhombicuboctahedral prisms. In the process some of the cubical cells blend out. Alternatively, it can be thought of as a blend of four small cubicuboctahedral prisms. In the process the octagonal prism side cells blend with the base small cubicuboctahedra to produce the small rhombicuboctahedra.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 11: Antipodiumverts" (#449).

- Klitzing, Richard. "shafipto".