# Dodecagonal duotransitionalterprism

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Dodecagonal duotransitionalterprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 144 rectangular trapezoprisms, 24 dodecagonal prisms, 24 dodecagonal trapezorhombihedra |

Faces | 576 isosceles trapezoids, 288 rectangles, 144 squares, 48 dodecagons |

Edges | 288+576+576 |

Vertices | 576 |

Vertex figure | Isosceles trapezoidal pyramid |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Dodecagonal duotransitionaltertegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(12)≀S_{2}, order 1152 |

Convex | Yes |

Nature | Tame |

The **dodecagonal duotransitionalterprism** is a convex isogonal polychoron and the eleventh member of the duotransitionalterprism family. It consists of 24 dodecagonal trapezorhombihedra, 24 dodecagonal prisms, and 144 rectangular trapezoprisms. 2 dodecagonal trapezorhombihedra, 1 dodecagonal prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal dodecagonal-didoecagonal duoprisms. However, it cannot be made scaliform.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:2.36603.