# Hexagonal antiditetragoltriate

Jump to navigation
Jump to search

Hexagonal antiditetragoltriate | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Hadet |

Elements | |

Cells | 36+36 tetragonal disphenoids, 72 rectangular pyramids, 12 hexagonal prisms |

Faces | 144+144 isosceles triangles, 72 rectangles, 12 hexagons |

Edges | 72+72+144 |

Vertices | 72 |

Vertex figure | Biaugmented triangular prism |

Measures (based on same duoprisms as optimized hexagonal ditetragoltriate) | |

Edge lengths | Edges of smaller hexagon (72): 1 |

Lacing edges (144): | |

Edges of larger hexagon (72): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Hadet |

Regiment | Hadet |

Dual | Hexagonal antitetrambitriate |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | G_{2}≀S_{2}, order 288 |

Convex | Yes |

Nature | Tame |

The **hexagonal antiditetragoltriate** or **hadet** is a convex isogonal polychoron and the fourth member of the antiditetragoltriate family. It consists of 12 hexagonal prisms, 72 rectangular pyramids, and 72 tetragonal disphenoids of two kinds. 2 hexagonal prisms, 4 tetragonal disphenoids, and 5 rectangular pyramids join at each vertex. However, it cannot be made scaliform.

It can be formed as the convex hull of 2 oppositely oriented semi-uniform hexagonal duoprisms where the larger hexagon is more than times the edge length of the smaller one.