# Great heptagrammic prism

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Great heptagrammic prism | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Giship |

Info | |

Coxeter diagram | x x7/3o |

Symmetry | I2(7)×A1, order 28 |

Army | Semi-uniform Hep |

Regiment | Giship |

Elements | |

Vertex figure | Isosceles triangle, edge lengths √2, √2, 2cos(3π/7) |

Faces | 7 squares, 2 great heptagrams |

Edges | 7+14 |

Vertices | 14 |

Measures (edge length 1) | |

Circumradius | √1+1/sin^{2}(3π/7)/2 ≈ 0.71626 |

Volume | 7/(4tan(3π/7)) ≈ 0.39943 |

Dihedral angles | 4–7/3: 90° |

4–4: π/7 ≈ 25.71429° | |

Height | 1 |

Central density | 3 |

Euler characteristic | 2 |

Related polytopes | |

Dual | Great heptagrammic bipyramid |

Conjugates | Heptagonal prism, Heptagrammic prism |

Convex core | Heptagonal prism |

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **great heptagrammic prism**, or **giship**, is a prismatic uniform polyhedron. It consists of 2 great heptagrams and 7 squares. Each vertex joins one great heptagram and two squares. As the name suggests, it is a prism based on a great heptagram.

## Vertex coordinates[edit | edit source]

The coordinates of a great heptagrammic prism, centered at the origin and with edge length 2sin(3π/7), are given by:

- (1, 0, ±sin(3π/7)),
- (cos(2π/7), ±sin(2π/7), ±sin(3π/7)),
- (cos(4π/7), ±sin(4π/7), ±sin(3π/7)),
- (cos(6π/7), ±sin(6π/7), ±sin(3π/7)).

## External links[edit | edit source]

- Klitzing, Richard. "Giship".

- Wikipedia Contributors. "Heptagrammic prism (7/3)".