# Biheptagonal duotransitionalterprism

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Biheptagonal duotransitionalterprism | |
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File:Biheptagonal duotransitionalterprism.png | |

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 49 rectangular trapezoprisms, 14 diheptagonal prisms, 14 orthoaligned truncated heptagonal prisms |

Faces | 196 isosceles trapezoids, 98+98 rectangles, 49 ditetragons, 28 diheptagons |

Edges | 196+196+196+196 |

Vertices | 392 |

Vertex figure | Irregular tetrahedron |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Biheptagonal duotransitionaltertegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(7)≀S_{2}, order 392 |

Convex | Yes |

Nature | Tame |

The **biheptagonal duotransitionalterprism** is a convex isogonal polychoron and the sixth member of the bipolygonal duotransitionalterprism family. It consists of 14 orthoaligned truncated heptagonal prisms, 14 diheptagonal prisms, and 49 rectangular trapezoprisms. 2 orthoaligned truncated heptagonal prisms, 1 diheptagonal prism, and 1 rectangular trapezoprism join at each vertex. It can be obtained as the convex hull of two orthogonal diheptagonal-diheptagonal duoprisms. However, it cannot be made scaliform.

This polychoron can be alternated into a snub heptagonal duotransitionalterprism, which is also not scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:2.27416.

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