# Decagonal duotransitionalterprism

Jump to navigation
Jump to search

Decagonal duotransitionalterprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 100 rectangular trapezoprisms, 20 decagonal prisms, 20 decagonal trapezorhombihedra |

Faces | 400 isosceles trapezoids, 200 rectangles, 100 squares, 40 decagons |

Edges | 200+400+400 |

Vertices | 400 |

Vertex figure | Isosceles trapezoidal pyramid |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Decagonal duotransitionaltertegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(10)≀S_{2}, order 800 |

Convex | Yes |

Nature | Tame |

The **decagonal duotransitionalterprism** is a convex isogonal polychoron and the ninth member of the duotransitionalterprism family. It consists of 20 decagonal trapezorhombihedra, 20 decagonal prisms, and 100 rectangular trapezoprisms. 2 decagonal trapezorhombihedra, 1 decagonal prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal decagonal-didecagonal duoprisms. However, it cannot be made scaliform.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:2.34500.