# Heptagonal duoprismatic prism

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Heptagonal duoprismatic prism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Hehep |

Coxeter diagram | x x7o x7o |

Elements | |

Tera | 14 square-heptagonal duoprisms, 2 heptagonal duoprisms |

Cells | 49 cubes, 14+28 heptagonal prisms, |

Faces | 98+98 squares, 28 heptagons |

Edges | 49+196 |

Vertices | 98 |

Vertex figure | Tetragonal disphenoidal pyramid, edge lengths 2cos(π/7) (disphenoid bases) and √2 (remaining edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Squahedip–hep–squahedip: |

Squahedip–cube–squahedip: 90° | |

Hedip–hep–squahedip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 16 |

Level of complexity | 15 |

Related polytopes | |

Army | Hehep |

Regiment | Hehep |

Dual | Heptagonal duotegmatic tegum |

Conjugates | Heptagrammic duoprismatic prism, Great heptagrammic duoprismatic prism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(7)≀S_{2}×A_{1}, order 784 |

Convex | Yes |

Nature | Tame |

The **heptagonal duoprismatic prism** or **hehep**, also known as the **heptagonal-heptagonal prismatic duoprism**, is a convex uniform duoprism that consists of 2 heptagonal duoprisms and 14 square-heptagonal duoprisms. Each vertex joins 4 square-heptagonal duoprisms and 1 heptagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

## Vertex coordinates[edit | edit source]

The vertices of a heptagonal duoprismatic prism of edge length 2sin(π/7) are given by:

where j, k = 2, 4, 6.

## Representations[edit | edit source]

A heptagonal duoprismatic prism has the following Coxeter diagrams:

- x x7o x7o (full symmetry)
- xx7oo xx7oo&#x (heptagonal duoprism atop heptagonal duoprism)