# Square-enneagrammic duoprism

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Square-enneagrammic duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Sastedip |

Info | |

Coxeter diagram | x4o x9/2o |

Symmetry | BC2×I2(9), order 144 |

Army | Semi-uniform sendip |

Regiment | Sastedip |

Elements | |

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

Cells | 9 cubes, 4 enneagrammic prisms |

Faces | 9+36 squares, 4 enneagrammic prisms |

Edges | 36+36 |

Vertices | 36 |

Measures (edge length 1) | |

Circumradius | √2+csc^{2}(2π/9)/2 ≈ 1.05122 |

Hypervolume | 9/[4tan(2π/9)] ≈ 2.68145 |

Dichoral angles | Cube–4–cube: 100° |

Step–9/2–step: 90° | |

Cube–4–step: 90° | |

Central density | 2 |

Related polytopes | |

Dual | Square-enneagrammic duotegum |

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

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **square-enneagrammic duoprism**, also known as **sastedip** or the **4-9/2 duoprism**, is a uniform duoprism that consists of 9 cubes and 4 enneagrammic prisms, with 2 of each meeting at each vertex.

The name can also refer to the square-great enneagrammic duoprism, which uses a different stellation of the enneagon.

## Vertex coordinates[edit | edit source]

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

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

## External links[edit | edit source]

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

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