# Hexagonal antifastegium

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Hexagonal antifastegium | |
---|---|

Rank | 4 |

Type | Segmentotope |

Notation | |

Bowers style acronym | Haf |

Coxeter diagram | ox xo6ox&#x |

Elements | |

Cells | 6 tetrahedra, 6 square pyramids, 1 hexagonal prism, 2 hexagonal antiprisms |

Faces | 12+12+12 triangles, 6 squares, 1+2 hexagons |

Edges | 6+6+12+24 |

Vertices | 6+12 |

Vertex figures | 6 wedges, edge lengths √3 (top) and 1 (remaining edges) |

12 isosceles trapezoidal pyramids, base edge lengths 1, 1, 1, √3, side edge lengths 1, 1, √2, √2 | |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Tet–3–squippy: |

Hip–4–squippy: | |

Hap–3–tet: | |

Hap–3–squippy: | |

Hap–6–hap: | |

Hip–6–hap: | |

Heights | Hig atop hap: |

Hig atop gyro hip: | |

Central density | 1 |

Related polytopes | |

Army | Haf |

Regiment | Haf |

Dual | Hexagonal antitegmatonotch |

Conjugate | Hexagonal antifastegium |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | G_{2}×A_{1}×I, order 24 |

Convex | Yes |

Nature | Tame |

The **hexagonal antifastegium**, or **haf**, is a CRF segmentochoron (designated K-4.46 on Richard Klitzing's list). It consists of 1 hexagonal prism, 2 hexagonal antiprisms, 6 tetrahedra, and 6 square pyramids. It is a member of the infinite family of polygonal antifastegiums.

It is a segmentochoron between a hexagon and a hexagonal antiprism or between a hexagon and a gyro hexagonal prism.

## Vertex coordinates[edit | edit source]

The vertices of a hexagonal antifastegium of edge length 1 are given by:

## Representations[edit | edit source]

The hexagonal antifastegium can be represented by the following Coxeter diagrams:

- ox xo6ox&#x
- xoo6oxx&#x

## External links[edit | edit source]

- Klitzing, Richard. "haf".