# Square-small hendecagrammic duoprism

(Redirected from 11/2-4 duoprism)

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

Rank | 4 |

Type | Uniform |

Space | Spherical |

Info | |

Coxeter diagram | x4o x11/2o |

Symmetry | BC2×I2(11), order 176 |

Army | Semi-uniform shendip |

Elements | |

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

Cells | 11 cubes, 4 small hendecagrammic prisms |

Faces | 11+44 squares, 4 small hendecagrams |

Edges | 44+44 |

Vertices | 44 |

Measures (edge length 1) | |

Circumradius | √2+csc^{2}(2π/11)/2 ≈ 1.16418 |

Hypervolume | 11/[4tan(2π/11)] ≈ 4.27908 |

Dichoral angles | Cube–4–cube: 7π/11 ≈ 114.54545° |

11/2p–11/2–11/2p: 90° | |

Cube–4–11/2p: 90° | |

Central density | 2 |

Related polytopes | |

Dual | Square-small hendecagrammic duotegum |

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

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

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

## Vertex coordinates[edit | edit source]

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

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

## External links[edit | edit source]

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

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