# Triangular duotransitionalterprism

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Triangular duotransitionalterprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 6 triangular prisms, 9 rectangular trapezoprisms, 6 triangular trapezorhombihedra |

Faces | 12 triangles, 36 isosceles trapezoids, 18 rectangles, 9 squares |

Edges | 18+36+36 |

Vertices | 36 |

Vertex figure | Isosceles trapezoidal pyramid |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Triangular duotransitionaltertegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{2}≀S_{2}, order 72 |

Convex | Yes |

Nature | Tame |

The **triangular duotransitionalterprism** is a convex isogonal polychoron and the second member of the duotransitionalterprism family. It consists of 6 triangular trapezorhombihedra, 6 triangular prisms, and 9 rectangular trapezoprisms. 2 triangular trapezorhombihedra, 1 triangular prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal triangular-hexagonal duoprisms. However, it cannot be made scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.70711.