# Hexagonal duoantiprism

The **hexagonal duoantiprism** or **hiddap**, also known as the **hexagonal-hexagonal duoantiprism**, the **6 duoantiprism** or the **6-6 duoantiprism**, is a convex isogonal polychoron that consists of 24 hexagonal antiprisms and 72 tetragonal disphenoids. 4 hexagonal antiprisms and 4 tetragonal disphenoids join at each vertex. It can be obtained through the process of alternating the dodecagonal duoprism. However, it cannot be made uniform, and has two edge lengths. It is the second in an infinite family of isogonal hexagonal dihedral swirlchora.

Hexagonal duoantiprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Hiddap |

Coxeter diagram | s12o2s12o () |

Elements | |

Cells | 72 tetragonal disphenoids, 24 hexagonal antiprisms |

Faces | 288 isosceles triangles, 24 hexagons |

Edges | 144+144 |

Vertices | 72 |

Vertex figure | Gyrobifastigium |

Measures (based on hexagons of edge length 1) | |

Edge lengths | Lacing (144): |

Edges of hexagons (144): 1 | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Hiddap |

Regiment | Hiddap |

Dual | Hexagonal duoantitegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | (I_{2}(12)≀S_{2})/2, order 576 |

Convex | Yes |

Nature | Tame |

The ratio between the longest and shortest edges is 1: ≈ 1:1.36603.

## Vertex coordinates Edit

The vertices of a hexagonal duoantiprism based on hexagons of edge length 1, centered at the origin, are given by: