# Enneagonal duoprismatic prism

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Enneagonal duoprismatic prism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Eep |

Coxeter diagram | x x9o x9o () |

Elements | |

Tera | 18 square-enneagonal duoprisms, 2 enneagonal duoprisms |

Cells | 81 cubes, 18+36 enneagonal prisms |

Faces | 162+162 squares, 36 enneagons |

Edges | 81+324 |

Vertices | 162 |

Vertex figure | Tetragonal disphenoidal pyramid, edge lengths 2cos(π/9) (disphenoid bases) and √2 (remaining edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Sendip–ep–sendip: 140° |

Sendip–cube–sendip: 90° | |

Edip–ep–sendip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 20 |

Level of complexity | 15 |

Related polytopes | |

Army | Eep |

Regiment | Eep |

Dual | Enneagonal duotegmatic tegum |

Conjugates | Enneagrammic duoprismatic prism, Great enneagrammic duoprismatic prism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(9)≀S_{2}×A_{1}, order 1296 |

Convex | Yes |

Nature | Tame |

The **enneagonal duoprismatic prism** or **eep**, also known as the **enneagonal-enneagonal prismatic duoprism**, is a convex uniform duoprism that consists of 2 enneagonal duoprisms and 18 square-enneagonal duoprisms. Each vertex joins 4 square-enneagonal duoprisms and 1 enneagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

## Vertex coordinates[edit | edit source]

The vertices of an enneagonal duoprismatic prism of edge length 2sin(π/9) are given by:

where j, k = 2, 4, 8.

## Representations[edit | edit source]

An enneagonal duoprismatic prism has the following Coxeter diagrams:

- x x9o x9o () (full symmetry)
- xx9oo xx9oo&#x (enneagonal duoprism atop enneagonal duoprism)