# Heptagonal prism

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

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Hep |

Coxeter diagram | x x7o () |

Conway notation | P7 |

Elements | |

Faces | 7 squares, 2 heptagons |

Edges | 7+14 |

Vertices | 14 |

Vertex figure | Isosceles triangle, edge lengths √2, √2, 2cos(π/7) |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–4: |

4–7: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 9 |

Level of complexity | 3 |

Related polytopes | |

Army | Hep |

Regiment | Hep |

Dual | Heptagonal tegum |

Conjugates | Heptagrammic prism, Great heptagrammic prism |

Abstract & topological properties | |

Flag count | 84 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Skeleton | GP(7,1) |

Properties | |

Symmetry | I_{2}(7)×A_{1}, order 28 |

Convex | Yes |

Nature | Tame |

The **heptagonal prism**, or **hep**, is a prismatic uniform polyhedron. It consists of 2 heptagons and 7 squares. Each vertex joins one heptagon and two squares. As the name suggests, it is a prism based on a heptagon.

## Vertex coordinates[edit | edit source]

The coordinates of a heptagonal prism, centered at the origin and with edge length 2sin(π/7), are given by:

- ,
- ,
- ,
- .

## External links[edit | edit source]

- Klitzing, Richard. "hep".
- Quickfur. "The Heptagonal Prism".

- Wikipedia contributors. "Heptagonal prism".
- McCooey, David. "Heptagonal Prism"