# Pentagonal-great heptagrammic duoprism

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

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Pagishdip |

Info | |

Coxeter diagram | x5o x7/3o |

Symmetry | H2×I2(7), order 140 |

Army | Semi-uniform pheddip |

Regiment | Pagishdip |

Elements | |

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

Cells | 7 pentagonal prisms, 5 great heptagrammic prisms |

Faces | 35 squares, 7 pentagons, 5 great heptagrams |

Edges | 35+35 |

Vertices | 35 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Pip–5–pip: π/7 ≈ 25.71429° |

Giship–7/3–giship: 108° | |

Pip–4–giship: 90° | |

Central density | 3 |

Related polytopes | |

Dual | Pentagonal-great heptagrammic duotegum |

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

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **pentagonal-great heptagrammic duoprism**, also known as **pagishdip** or the **5-7/3 duoprism**, is a uniform duoprism that consists of 7 pentagonal prisms and 5 great heptagrammic prisms, with two of each meeting at each vertex.

## Vertex coordinates[edit | edit source]

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

- (±sin(3π/7), –sin(3π/7)√(5+2√5)/5, 1, 0),
- (±sin(3π/7), –sin(3π/7)√(5+2√5)/5, cos(2π/7), ±sin(2π/7)),
- (±sin(3π/7), –sin(3π/7)√(5+2√5)/5, cos(4π/7), ±sin(4π/7)),
- (±sin(3π/7), –sin(3π/7)√(5+2√5)/5, cos(6π/7), ±sin(6π/7)),
- (±(1+√5)sin(3π/7)/2, sin(3π/7)√(5–√5)/10, 1, 0),
- (±(1+√5)sin(3π/7)/2, sin(3π/7)√(5–√5)/10, cos(2π/7), ±sin(2π/7)),
- (±(1+√5)sin(3π/7)/2, sin(3π/7)√(5–√5)/10, cos(4π/7), ±sin(4π/7)),
- (±(1+√5)sin(3π/7)/2, sin(3π/7)√(5–√5)/10, cos(6π/7), ±sin(6π/7)),
- (0, 2sin(3π/7)√(5+√5)/10, 1, 0),
- (0, 2sin(3π/7)√(5+√5)/10, cos(2π/7), ±sin(2π/7)),
- (0, 2sin(3π/7)√(5+√5)/10, cos(4π/7), ±sin(4π/7)),
- (0, 2sin(3π/7)√(5+√5)/10, cos(6π/7), ±sin(6π/7)).

## External links[edit | edit source]

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

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