# Small circumfacetodistetracontoctachoron

The **small circumfacetodistetracontoctachoron**, or **smiffadic**, is a nonconvex uniform polychoron that consists of 48 octahedra and 48 small rhombicuboctahedra. Two octahedra and eight small rhombicuboctahedra join at each vertex.

Small circumfacetodistetracontoctachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Smiffadic |

Elements | |

Cells | 48 octahedra, 48 small rhombicuboctahedra |

Faces | 384 triangles, 144+288 squares |

Edges | 576 |

Vertices | 144 |

Edge figure | (oct 3 sirco 4 sirco 4 sirco 4 sirco 3) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Sirco–3–oct: 120° |

Sirco–4–sirco: 90° | |

Number of external pieces | 1008 |

Level of complexity | 14 |

Related polytopes | |

Army | Spic |

Regiment | Spic |

Conjugate | Great intercepted distetracontoctachoron |

Abstract & topological properties | |

Flag count | 11520 |

Euler characteristic | 288 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | No |

Nature | Wild |

It also has triangular prisms as pseudofacets.

## Vertex coordinates edit

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

## External links edit

- Bowers, Jonathan. "Category 13: Spic and Giddic Regiments" (#515).

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