# Square-enneagonal duoprism

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Square-enneagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Sendip |

Info | |

Coxeter diagram | x4o x9o |

Symmetry | BC2×I2(9), order 144 |

Army | Sendip |

Regiment | Sendip |

Elements | |

Vertex figure | Digonal disphenoid, edge lengths 2cos(π/9) (base 1) and √2 (base 2 and sides) |

Cells | 9 cubes, 4 enneagonal prisms |

Faces | 9+36 squares, 4 enneagons |

Edges | 36+36 |

Vertices | 36 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Cube–4–cube: 140° |

Cube–4–ep: 90° | |

Ep–9–ep: 90° | |

Height | 1 |

Central density | 1 |

Euler characteristic | 0 |

Number of pieces | 13 |

Level of complexity | 6 |

Related polytopes | |

Dual | Square-enneagonal duotegum |

Conjugates | Square-enneagrammic duoprism, Square-great enneagrammic duoprism |

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **square-enneagonal duoprism** or **sendip**, also known as the **4-9 duoprism**, is a uniform duoprism that consists of 4 enneagonal prisms and 9 cubes, with two of each joining at each vertex. It is also a convex segmentochoron, being the prism of the enneagonal prism.

## Vertex coordinates[edit | edit source]

The coordinates of a square-enneagonal duoprism, centered at the origin and with edge length 2sin(π/9), are given by:

- (±sin(π/9), ±sin(π/9), 1, 0),
- (±sin(π/9), ±sin(π/9), cos(2π/9), ±sin(2π/9)),
- (±sin(π/9), ±sin(π/9), cos(4π/9), ±sin(4π/9)),
- (±sin(π/9), ±sin(π/9), –1/2, ±√3/2),
- (±sin(π/9), ±sin(π/9), cos(8π/9), ±sin(8π/9)).

## Representations[edit | edit source]

A square-enneagonal duoprism has the following Coxeter diagrams:

- x4o x9o (full symmetry)
- x x x9o (squares as rectangles)

## External links[edit | edit source]

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