# Octagonal duoprismatic prism

Octagonal duoprismatic prism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Oop |

Coxeter diagram | x x8o x8o () |

Elements | |

Tera | 16 square-octagonal duoprisms, 2 octagonal duoprisms |

Cells | 64 cubes, 16+32 octagonal prisms |

Faces | 128+128 squares, 32 octagons |

Edges | 64+256 |

Vertices | 128 |

Vertex figure | Tetragonal disphenoidal pyramid, edge lengths √2+√2 (disphenoid bases) and √2 (remaining edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Sodip–op–sodip: 135° |

Sodip–cube–sodip: 90° | |

Odip–op–sodip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 18 |

Level of complexity | 15 |

Related polytopes | |

Army | Oop |

Regiment | Oop |

Dual | Octagonal duotegmatic tegum |

Conjugate | Octagrammic duoprismatic prism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(8)≀S_{2}×A_{1}, order 1024 |

Convex | Yes |

Nature | Tame |

The **octagonal duoprismatic prism** or **oop**, also known as the **octagonal-octagonal prismatic duoprism**, is a convex uniform duoprism that consists of 2 octagonal duoprisms and 16 square-octagonal duoprisms. Each vertex joins 4 square-octagonal duoprisms and 1 octagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

The octagonal duoprismatic prism can be vertex-inscribed into a small prismated penteract.

This polyteron can be alternated into a square duoantiprismatic antiprism, although it cannot be made uniform. Half of the octagons can also be alternated into long rectangles to create a square-square prismatic prismantiprismoid, which is also nonuniform.

## Vertex coordinates[edit | edit source]

The vertices of a octagonal duoprismatic prism of edge length 1 are given by:

- ,
- ,
- ,
- .

## Representations[edit | edit source]

An octagonal duoprismatic prism has the following Coxeter diagrams:

- x x8o x8o () (full symmetry)
- x x4x x4x () (octagons as ditetragons)
- xx8oo xx8oo&#x (octagonal duoprism atop octagonal duoprism)
- xx4xx xx4xx&#x