# Octagonal-dodecagonal duoprismatic prism

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

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Otwip |

Coxeter diagram | x x8o x12o |

Elements | |

Tera | 12 square-octagonal duoprisms, 8 square-dodecagonal duoprisms, 2 octagonal-dodecagonal duoprisms |

Cells | 96 cubes, 8+16 dodecagonal prisms, 12+24 octagonal prisms |

Faces | 96+96+192 squares, 24 octagons, 16 dodecagons |

Edges | 96+192+192 |

Vertices | 192 |

Vertex figure | Digonal disphenoidal pyramid, edge lengths √2+√2 (disphenoid base 1), √2+√3 (disphenoid base 2), √2 (remaining edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Sodip–op–sodip: 150° |

Sitwadip–twip–sitwadip: 135° | |

Sitwadip–cube–sodip: 90° | |

Otwadip–op–sodip: 90° | |

Sitwadip–twip–otwadip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 22 |

Level of complexity | 30 |

Related polytopes | |

Army | Otwip |

Regiment | Otwip |

Dual | Octagonal-dodecagonal duotegmatic tegum |

Conjugates | Octagonal-dodecagrammic duoprismatic prism, Octagrammic-dodecagonal duoprismatic prism, Octagrammic-dodecagrammic duoprismatic prism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(8)×I_{2}(12)×A_{1}, order 768 |

Convex | Yes |

Nature | Tame |

The **octagonal-dodecagonal duoprismatic prism** or **otwip**, also known as the **octagonal-dodecagonal prismatic duoprism**, is a convex uniform duoprism that consists of 2 octagonal-dodecagonal duoprisms, 8 square-dodecagonal duoprisms, and 12 square-octagonal duoprisms. Each vertex joins 2 square-octagonal duoprisms, 2 square-dodecagonal duoprisms, and 1 octagonal-dodecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

This polyteron can be alternated into a square-hexagonal duoantiprismatic antiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a hexagonal-square prismatic prismantiprismoid or the dodecagons into long ditrigons to create a square-hexagonal prismatic prismantiprismoid, which are also both nonuniform.

## Vertex coordinates[edit | edit source]

The vertices of an octagonal-dodecagonal duoprismatic prism of edge length 1 are given by all permutations of the first two coordinates of:

## Representations[edit | edit source]

An octagonal-dodecagonal duoprismatic prism has the following Coxeter diagrams:

- x x8o x12o (full symmetry)
- x x4x x12o (octagons as ditetragons)
- x x8o x6x (dodecagons as dihexagons)
- x x4x x6x
- xx8oo xx12oo&#x (octagonal-enneagonal duoprism atop octagonal-enneagonal duoprism)
- xx4xx xx12oo&#x
- xx8oo xx6xx&#x
- xx4xx xx6xx&#x