# Square-heptagrammic duoprism

(Redirected from 7/2-4 duoprism)

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Square-heptagrammic duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Sashedip |

Info | |

Coxeter diagram | x4o x7/2o |

Symmetry | BC2×I2(7), order 112 |

Army | Semi-uniform squahedip |

Regiment | Sashedip |

Elements | |

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

Cells | 7 cubes, 4 heptagrammic prisms |

Faces | 7+28 squares, 4 heptagrams |

Edges | 28+28 |

Vertices | 28 |

Measures (edge length 1) | |

Circumradius | √2+csc^{2}(2π/7)/2 ≈ 0.95341 |

Hypervolume | 7/[4tan(2π/7)] ≈ 1.39558 |

Dichoral angles | Cube–4–cube: 3π/7 ≈ 77.14286° |

Ship–7/2–ship: 90° | |

Cube–4–ship: 90° | |

Central density | 2 |

Related polytopes | |

Dual | Square-heptagrammic duotegum |

Conjugates | Square-heptagonal duoprism, Square-great heptagrammic duoprism |

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **square-heptagrammic duoprism**, also known as **sashedip** or the **4-7/2 duoprism**, is a uniform duoprism that consists of 7 cubes and 4 heptagrammic prisms, with 2 of each meeting at each vertex.

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

## Vertex coordinates[edit | edit source]

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

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

## External links[edit | edit source]

Bowers, Jonathan. "Category A: Duoprisms".

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