# Pentagonal duotransitionalterprism

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Pentagonal duotransitionalterprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 25 rectangular trapezoprisms, 10 pentagonal prisms, 10 pentagonal trapezorhombihedra |

Faces | 100 isosceles trapezoids, 50 rectangles, 25 squares, 20 pentagons |

Edges | 50+100+100 |

Vertices | 100 |

Vertex figure | Isosceles trapezoidal pyramid |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Pentagonal duotransitionaltertegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{2}≀S_{2}, order 200 |

Convex | Yes |

Nature | Tame |

The **pentagonal duotransitionalterprism** is a convex isogonal polychoron and the fourth member of the duotransitionalterprism family. It consists of 10 pentagonal trapezorhombihedra, 10 pentagonal prisms, and 25 rectangular trapezoprisms. 2 pentagonal trapezorhombihedra, 1 pentagonal prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal pentagonal-dipentagonal duoprisms. However, it cannot be made scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:2.14412.