# Great hexadecafaceted prismatotesseractioctachoron

Great hexadecafaceted prismatotesseractioctachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gahfipto |

Coxeter diagram | |

Elements | |

Cells | 32 triangular prisms, 8 cubes, 8 quasirhombicuboctahedra |

Faces | 64 triangles, 48+96 squares |

Edges | 96+96 |

Vertices | 64 |

Vertex figure | Triangular hemipodium, edge lengths √2 (top triangle and sides) and 1 (base pseudo-triangle) |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Querco–4–cube: 90° |

Querco–3–trip: 90° | |

Querco–4–trip: | |

Number of external pieces | 2824 |

Level of complexity | 343 |

Related polytopes | |

Army | Tat |

Regiment | Gittith |

Conjugate | Small hexadecafaceted prismatotesseractioctachoron |

Abstract & topological properties | |

Euler characteristic | 32 |

Orientable | No |

Properties | |

Symmetry | B_{4}, order 384 |

Convex | No |

Nature | Tame |

The **great hexadecafaceted prismatotesseractioctachoron**, or **gahfipto**, is a nonconvex uniform polychoron that consists of 8 quasirhombicuboctahedra, 8 cubes, and 32 triangular prisms. Three quasirhombicuboctahedra, one cube, and three triangular prisms join at each vertex.

It also has 16 tetrahedra and 24 cubes as pseudofacets.

It can be constructed as a blend of four quasirhombicuboctahedral prisms. In the process some of the cubical cells blend out. Alternatively, it can be thought of as a blend of four great cubicuboctahedral prisms. In the process the octagrammic prism side cells blend with the base great cubicuboctahedra to produce the quasirhombicuboctahedra.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the great tesseractitesseractihexadecachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 12: Podiumverts" (#488).

- Klitzing, Richard. "gahfipto".