# Square-hendecagrammic duoprism

(Redirected from 11/3-4 duoprism)

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Square-hendecagrammic duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Info | |

Coxeter diagram | x4o x11/3o |

Symmetry | BC2×I2(11), order 176 |

Army | Semi-uniform shendip |

Elements | |

Vertex figure | Digonal disphenoid, edge lengths 2cos(3π/11) (base 1) and √2 (base 2 and sides) |

Cells | 11 cubes, 4 hendecagrammic prisms |

Faces | 11+44 squares, 4 hendecagrams |

Edges | 44+44 |

Vertices | 44 |

Measures (edge length 1) | |

Circumradius | √2+csc^{2}(3π/11)/2 ≈ 0.96835 |

Hypervolume | 11/[4tan(3π/11)] ≈ 2.38289 |

Dichoral angles | Cube–4–cube: 5π/11 ≈ 81.81818° |

11/3p–11/3–11/3p: 90° | |

Cube–4–11/3p: 90° | |

Central density | 3 |

Related polytopes | |

Dual | Square-hendecagrammic duotegum |

Conjugates | Square-hendecagonal duoprism, Square-small hendecagrammic duoprism, Square-great hendecagrammic duoprism, Square-grand hendecagrammic duoprism |

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **square-hendecagrammic duoprism**, also known as the **4-11/3 duoprism**, is a uniform duoprism that consists of 11 cubes and 4 hendecagrammic prisms, with 2 of each meeting at each vertex.

The name can also refer to the square-small hendecagrammic duoprism, square-great hendecagrammic duoprism, or the square-grand hendecagrammic duoprism.

## Vertex coordinates[edit | edit source]

The coordinates of a square-hendecagrammic duoprism, centered at the origin and with edge length 2sin(3π/11), are given by:

- (±sin(3π/11), ±sin(3π/11), 1, 0),
- (±sin(3π/11), ±sin(3π/11), cos(2π/11), ±sin(2π/11)),
- (±sin(3π/11), ±sin(3π/11), cos(4π/11), ±sin(4π/11)),
- (±sin(3π/11), ±sin(3π/11), cos(6π/11), ±sin(6π/11)),
- (±sin(3π/11), ±sin(3π/11), cos(8π/11), ±sin(8π/11)),
- (±sin(3π/11), ±sin(3π/11), cos(10π/11), ±sin(10π/11)).

## External links[edit | edit source]

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

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