# Antifrustary distetracontoctachoron

Antifrustary distetracontoctachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Afdec |

Coxeter diagram | x3o4x3o4*a4/3*c () |

Elements | |

Cells | 48 cuboctahedra, 48 great cubicuboctahedra |

Faces | 384 triangles, 288 squares, 144 octagrams |

Edges | 1152 |

Vertices | 288 |

Vertex figure | Rectangular trapezoprism, edge lengths 1 and √2 (base) and √2–√2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Gocco–8/3–gocco: 135° |

Co–4–gocco: 135° | |

Co–3–gocco: 120° | |

Central density | 5 |

Related polytopes | |

Army | Cont, edge length |

Regiment | Afdec |

Conjugate | Great retrofrustary distetracontoctachoron |

Abstract & topological properties | |

Flag count | 13824 |

Euler characteristic | –144 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | No |

Nature | Tame |

The **antifrustary distetracontoctachoron**, or **afdec**, is a nonconvex uniform polychoron that consists of 48 cuboctahedra and 48 great cubicuboctahedra. 2 cuboctahedra and 4 great cubicuboctahedra join at each vertex.

The antifrustary distetracontoctachoron contains the vertices of a hexagonal duoprism, small skewverted prismatohexadecadisoctachoron, octagonal-octagrammic duoprism, and cuboctatruncated cuboctahedral prism.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of an antifrustary distetracontoctachoron of edge length 1 are all permutations of:

The second set of vertices are identical to those of an inscribed small skewverted prismatohexadecadisoctachoron.

## Related polychora[edit | edit source]

The antifrustary distetracontoctaachoron is the colonel of a regiment that contains 53 uniform members, along with one fissary and one compound. 7 uniform members, plus the fissary and compound have full symmetry, while the other facetings have a single F4 symmetry only.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 15: Afdec Regiment" (#612).

- Klitzing, Richard. "afdec".