# Heptagonal-tetrahedral duoprism

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Heptagonal-tetrahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Hetet |

Coxeter diagram | x7o x3o3o |

Elements | |

Tera | 7 tetrahedral prisms, 4 triangular-heptagonal duoprisms |

Cells | 7 tetrahedra, 28 triangular prisms, 6 heptagonal prisms |

Faces | 28 triangles, 42 squares, 4 heptagons |

Edges | 28+42 |

Vertices | 28 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tepe–tet–tepe: |

Tepe–trip–theddip: 90° | |

Theddip–hep–theddip: | |

Heights | Heg atop theddip: |

Hep atop perp hep: | |

Central density | 1 |

Number of external pieces | 11 |

Level of complexity | 10 |

Related polytopes | |

Army | Hetet |

Regiment | Hetet |

Dual | Heptagonal-tetrahedral duotegum |

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

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}×I2(7), order 336 |

Convex | Yes |

Nature | Tame |

The **heptagonal-tetrahedral duoprism** or **hetet** is a convex uniform duoprism that consists of 7 tetrahedral prisms and 4 triangular-heptagonal duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular-heptagonal duoprisms.

## Vertex coordinates[edit | edit source]

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

where j = 2, 4, 6.