# Heptagrammic-octagrammic duoprism

(Redirected from 7/2-8/3 duoprism)

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Heptagrammic-octagrammic duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Shestodip |

Info | |

Coxeter diagram | x7/2o x8/3o |

Symmetry | I2(7)×I2(8), order 224 |

Army | Semi-uniform heodip |

Regiment | Shestodip |

Elements | |

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

Cells | 8 heptagrammic prisms, 7 octagrammic prisms |

Faces | 56 squares, 8 heptagrams, 7 octagrams |

Edges | 56+56 |

Vertices | 56 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Ship–7/2–ship: 45° |

Stop–8/3–stop: 3π/7 ≈ 77.14286° | |

Ship–4–stop: 90° | |

Central density | 6 |

Related polytopes | |

Dual | Heptagrammic-octagrammic duotegum |

Conjugates | Heptagonal-octagonal duoprism, Heptagonal-octagrammic duoprism, Heptagrammic-octagonal duoprism, Great heptagrammic-octagonal duoprism, Great heptagrammic-octagrammic duoprism |

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **heptagrammic-octagrammic duoprism**, also known as **shestodip** or the **7/2-8/3 duoprism**, is a uniform duoprism that consists of 8 heptagrammic prisms and 7 octagrammic prisms, with 2 of each meeting at each vertex.

The name can also refer to the great heptagrammic-octagrammic duoprism.

## Vertex coordinates[edit | edit source]

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

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

## External links[edit | edit source]

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

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