# Heptagonal-octahedral duoprism

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Heptagonal-octahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Heoct |

Coxeter diagram | x7o o4o3x |

Elements | |

Tera | 7 octahedral prisms, 8 triangular-heptagonal duoprisms |

Cells | 56 triangular prisms, 7 octahedra, 12 heptagonal prisms |

Faces | 56 triangles, 84 squares, 6 heptagons |

Edges | 42+84 |

Vertices | 42 |

Vertex figure | Square scalene, edge lengths 1 (base square), 2cos(π/7) (top), √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Ope–oct–ope: |

Theddip–hep–theddip: | |

Theddip–trip–ope: 90° | |

Central density | 1 |

Number of external pieces | 15 |

Level of complexity | 10 |

Related polytopes | |

Army | Heoct |

Regiment | Heoct |

Dual | Heptagonal-cubic duotegum |

Conjugates | Heptagrammic-octahedral duoprism, Great heptagrammic-octahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I2(7), order 672 |

Convex | Yes |

Nature | Tame |

The **heptagonal-octahedral duoprism** or **heoct** is a convex uniform duoprism that consists of 7 octahedral prisms and 8 triangular-heptagonal duoprisms. Each vertex joins 2 octahedral prisms and 4 triangular-heptagonal duoprisms.

## Vertex coordinates[edit | edit source]

The vertices of a heptagonal-octahedral duoprism of edge length 2sin(π/7) are given by all permutations and sign changes of the last three coordinates of:

where j = 2, 4, 6.