# Pentagonal-heptagonal duoprism

(Redirected from 7-5 duoprism)

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Pentagonal-heptagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Pheddip |

Info | |

Coxeter diagram | x5o x7o |

Symmetry | H2×I2(7), order 140 |

Army | Pheddip |

Regiment | Pheddip |

Elements | |

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

Cells | 7 pentagonal prisms, 5 heptagonal prisms |

Faces | 35 squares, 7 pentagons, 5 heptagons |

Edges | 35+35 |

Vertices | 35 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Pip–5–pip: |

Hep–7–hep: 108° | |

Pip–4–hep: 90° | |

Central density | 1 |

Euler characteristic | 0 |

Number of pieces | 12 |

Level of complexity | 6 |

Related polytopes | |

Dual | Pentagonal-heptagonal duotegum |

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

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **pentagonal-heptagonal duoprism** or **pheddip**, also known as the **5-7 duoprism**, is a uniform duoprism that consists of 5 heptagonal prisms and 7 pentagonal prisms, with two of each joining at each vertex.

## Vertex coordinates[edit | edit source]

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

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

## External links[edit | edit source]

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