# Octagonal duotransitionalterprism

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Octagonal duotransitionalterprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 64 rectangular trapezoprisms, 16 octagonal prisms, 16 octagonal trapezorhombihedra |

Faces | 256 isosceles trapezoids, 128 rectangles, 64 squares, 32 octagons |

Edges | 128+256+256 |

Vertices | 256 |

Vertex figure | Isosceles trapezoidal pyramid |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Octagonal duotransitionaltertegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(8)≀S_{2}, order 512 |

Convex | Yes |

Nature | Tame |

The **octagonal duotransitionalterprism** is a convex isogonal polychoron and the seventh member of the duotransitionalterprism family. It consists of 16 octagonal trapezorhombihedra, 16 octagonal prisms, and 64 rectangular trapezoprisms. 2 octagonal trapezorhombihedra, 1 octagonal prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal octagonal-dioctagonal duoprisms. However, it cannot be made scaliform.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:2.30656.