# Omnifacetodistetracontoctachoron

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Omnifacetodistetracontoctachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Offadac |

Elements | |

Cells | 48 truncated cubes, 48 small rhombicuboctahedra |

Faces | 384 triangles, 144+288 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 | |

Hypervolume | |

Dichoral angles | Sirco–4–sirco: 90° |

Sirco–3–tic: 60° | |

Tic–8–tic: 45° | |

Number of external pieces | 2496 |

Level of complexity | 29 |

Related polytopes | |

Army | Spic |

Regiment | Spic |

Conjugate | Polar facetodistetracontoctachoron |

Abstract & topological properties | |

Flag count | 16128 |

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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