# Pentagrammic-heptagonal duoprism

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Pentagrammic-heptagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Stahedip |

Info | |

Coxeter diagram | x5/2o x7o |

Symmetry | H2×I2(7), order 140 |

Army | Semi-uniform pheddip |

Regiment | Stahedip |

Elements | |

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

Cells | 7 pentagrammic prisms, 5 heptagonal prisms |

Faces | 35 squares, 7 pentagrams, 5 heptagons |

Edges | 35+35 |

Vertices | 35 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Stip–5/2–stip: 5π/7 ≈ 128.57143° |

Hep–7–hep: 36° | |

Stip–4–hep: 90° | |

Central density | 2 |

Related polytopes | |

Dual | Pentagrammic-heptagonal duotegum |

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

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

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

## Vertex coordinates[edit | edit source]

The coordinates of a pentagrammic-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)(√5–1)/2, sin(π/7)√(5+√5)/10, 1, 0),
- (±sin(π/7)(√5–1)/2, sin(π/7)√(5+√5)/10, cos(2π/7), ±sin(2π/7)),
- (±sin(π/7)(√5–1)/2, sin(π/7)√(5+√5)/10, cos(4π/7), ±sin(4π/7)),
- (±sin(π/7)(√5–1)/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".

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