# Hexagonal duotransitionalterprism

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Hexagonal duotransitionalterprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 36 rectangular trapezoprisms, 12 hexagonal prisms, 12 hexagonal trapezorhombihedra |

Faces | 144 isosceles trapezoids, 72 rectangles, 36 squares, 24 hexagons |

Edges | 72+144+144 |

Vertices | 144 |

Vertex figure | Isosceles trapezoidal pyramid |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Hexagonal duotransitionaltertegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | G_{2}≀S_{2}, order 288 |

Convex | Yes |

Nature | Tame |

The **hexagonal duotransitionalterprism** is a convex isogonal polychoron and the fifth member of the duotransitionalterprism family. It consists of 12 hexagonal trapezorhombihedra, 12 hexagonal prisms, and 36 rectangular trapezoprisms. 2 hexagonal trapezorhombihedra, 1 hexagonal prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal hexagonal-dihexagonal duoprisms. However, it cannot be made scaliform.

This polychoron can be alternated into a triangular duotransitionalterantiprism, which is also not scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:2.22474.