# Omnifacetodistetracontoctachoron

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Omnifacetodistetracontoctachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Offadac |

Elements | |

Cells | 48 tic, 48 sirco |

Faces | 384 triangles, 432 squares, 144 octagons |

Edges | 576 |

Vertices | 144 |

Vertex figure | Omnifaceted square antiprism |

Edge figure | (tic 8 tic 8 tic 3 sirco 4 sirco 4 sirco 4 sirco 3) |

Measures (edge length 1) | |

Circumradius | |

Number of external pieces | 2496 |

Level of complexity | 29 |

Related polytopes | |

Army | Spic |

Regiment | Spic |

Conjugate | Lifdic |

Abstract & topological properties | |

Euler characteristic | 432 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | No |

Nature | Wild |

The **omnifacetodistetracontoctachoron**, or **offadac**, is a nonconvex uniform polychoron that consists of 48 truncated cubes and 48 small rhombicuboctahedra. Eight truncated cubes and eight small rhombicuboctahedra join at each vertex.

It also has triangular prisms and doubly-covered tetrahemihexahedra as pseudofacets.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 13: Spic and Giddic Regiments" (#516).

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