# Pentagonal-heptagrammic duoprism

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Pentagonal-heptagrammic duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Pashedip |

Info | |

Coxeter diagram | x5o x7/2o |

Symmetry | H2×I2(7), order 140 |

Army | Semi-uniform pheddip |

Regiment | Pashedip |

Elements | |

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

Cells | 7 pentagonal prisms, 5 heptagrammic prisms |

Faces | 35 squares, 7 pentagons, 5 heptagrams |

Edges | 35+35 |

Vertices | 35 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Pip–5–pip: 3π/7 ≈ 77.14286° |

Ship–7/2–ship: 108° | |

Pip–4–ship: 90° | |

Central density | 2 |

Related polytopes | |

Dual | Pentagonal-heptagrammic duotegum |

Conjugates | Pentagonal-heptagonal duoprism, Pentagonal-great heptagrammic duoprism, Pentagrammic-heptagonal duoprism, Pentagrammic-heptagrammic duoprism, Pentagrammic-great heptagrammic duoprism |

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **pentagonal-heptagrammic duoprism**, also known as **pashedip** or the **5-7/2 duoprism**, is a uniform duoprism that consists of 7 pentagonal prisms and 5 heptagrammic prisms, with 2 of each meeting at each vertex.

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

## Vertex coordinates[edit | edit source]

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

- (±sin(2π/7), –sin(2π/7)√(5+2√5)/5, 1, 0),
- (±sin(2π/7), –sin(2π/7)√(5+2√5)/5, cos(2π/7), ±sin(2π/7)),
- (±sin(2π/7), –sin(2π/7)√(5+2√5)/5, cos(4π/7), ±sin(4π/7)),
- (±sin(2π/7), –sin(2π/7)√(5+2√5)/5, cos(6π/7), ±sin(6π/7)),
- (±(1+√5)sin(2π/7)/2, sin(2π/7)√(5–√5)/10, 1, 0),
- (±(1+√5)sin(2π/7)/2, sin(2π/7)√(5–√5)/10, cos(2π/7), ±sin(2π/7)),
- (±(1+√5)sin(2π/7)/2, sin(2π/7)√(5–√5)/10, cos(4π/7), ±sin(4π/7)),
- (±(1+√5)sin(2π/7)/2, sin(2π/7)√(5–√5)/10, cos(6π/7), ±sin(6π/7)),
- (0, 2sin(2π/7)√(5+√5)/10, 1, 0),
- (0, 2sin(2π/7)√(5+√5)/10, cos(2π/7), ±sin(2π/7)),
- (0, 2sin(2π/7)√(5+√5)/10, cos(4π/7), ±sin(4π/7)),
- (0, 2sin(2π/7)√(5+√5)/10, cos(6π/7), ±sin(6π/7)).

## External links[edit | edit source]

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

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