# Great heptagrammic-decagonal duoprism

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Great heptagrammic-decagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Gishdedip |

Info | |

Coxeter diagram | x7/3o x10o |

Symmetry | I2(7)×I2(10), order 280 |

Army | Semi-uniform hedadip |

Regiment | Gishdedip |

Elements | |

Vertex figure | Digonal disphenoid, edge lengths 2cos(3π/7) (base 1), √(5+√5)/2 (base 2), √2 (sides) |

Cells | 10 great heptagrammic prisms, 7 decagonal prisms |

Faces | 70 squares, 10 great heptagrams, 7 decagons |

Edges | 70+70 |

Vertices | 70 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Giship–7/3–giship: 144° |

Dip–10–dip: π/7 ≈ 25.71429° | |

Giship–4–dip: 90° | |

Central density | 3 |

Related polytopes | |

Dual | Great heptagrammic-decagonal duotegum |

Conjugates | Heptagonal-decagonal duoprism, Heptagonal-decagrammic duoprism, Heptagrammic-decagonal duoprism, Heptagrammic-decagrammic duoprism, Great heptagrammic-decagrammic duoprism |

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **great heptagrammic-decagonal duoprism**, also known as **gishdedip** or the **7/3-10 duoprism**, is a uniform duoprism that consists of 10 great heptagrammic prisms and 7 decagonal prisms, with 2 of each meeting at each vertex.

## Vertex coordinates[edit | edit source]

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

- (1, 0, ±sin(3π/7), ±sin(3π/7)√5+2√5),
- (1, 0, ±sin(3π/7)(3+√5)/2, ±sin(3π/7)√(5+√5)/2),
- (1, 0, ±sin(3π/7)(1+√5), 0),
- (cos(2π/7), ±sin(2π/7), ±sin(3π/7), ±sin(3π/7)√5+2√5),
- (cos(2π/7), ±sin(2π/7), ±sin(3π/7)(3+√5)/2, ±sin(3π/7)√(5+√5)/2),
- (cos(2π/7), ±sin(2π/7), ±sin(3π/7)(1+√5), 0),
- (cos(4π/7), ±sin(4π/7), ±sin(3π/7), ±sin(3π/7)√5+2√5),
- (cos(4π/7), ±sin(4π/7), ±sin(3π/7)(3+√5)/2, ±sin(3π/7)√(5+√5)/2),
- (cos(4π/7), ±sin(4π/7), ±sin(3π/7)(1+√5), 0),
- (cos(6π/7), ±sin(6π/7), ±sin(3π/7), ±sin(3π/7)√5+2√5),
- (cos(6π/7), ±sin(6π/7), ±sin(3π/7)(3+√5)/2, ±sin(3π/7)√(5+√5)/2),
- (cos(6π/7), ±sin(6π/7), ±sin(3π/7)(1+√5), 0).

## External links[edit | edit source]

- Bowers, Jonathan. "Category A: Duoprisms".

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