# Heptagonal duoexpandoprism

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Heptagonal duoexpandoprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Hedep |

Coxeter diagram | xo7xx ox7xx&#zy |

Elements | |

Cells | 49 tetragonal disphenoids, 98 wedges, 49 rectangular trapezoprisms, 14+14 heptagonal prisms |

Faces | 196 isosceles triangles, 196 isosceles trapezoids, 98+98 rectangles, 28 heptagons |

Edges | 98+98+196+196 |

Vertices | 196 |

Vertex figure | Mirror-symmetric triangular antiprism |

Measures (based on two heptagonal-tetradecagonal duoprisms of edge length 1) | |

Edge lengths | Edges of duoprisms (98+98+196): 1 |

Lacing edges (196): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Hedep |

Regiment | Hedep |

Dual | Heptagonal duoexpandotegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

The **heptagonal duoexpandoprism** or **hedep** is a convex isogonal polychoron and the sixth member of the duoexpandoprism family. It consists of 28 heptagonal prisms of two kinds, 49 rectangular trapezoprisms, 98 wedges, and 49 tetragonal disphenoids. 2 heptagonal prisms, 1 tetragonal disphenoid, 3 wedges, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal heptagonal-tetradecagonal duoprisms, or more generally heptagonal-diheptagonal duoprisms, and a subset of its variations can be constructed by expanding the cells of the heptagonal duoprism outward. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is .