# Octagonal-dodecagonal duoprism

Octagonal-dodecagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Otwadip |

Coxeter diagram | x8o x12o () |

Elements | |

Cells | 12 octagonal prisms, 8 dodecagonal prisms |

Faces | 96 squares, 12 octagons, 8 dodecagons |

Edges | 96+96 |

Vertices | 96 |

Vertex figure | Digonal disphenoid, edge lengths √2+√2 (base 1), (√2+√6)/2 (base 2), and √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Op–8–op: 150° |

Twip–12–twip: 135° | |

Op–4–twip: 90° | |

Central density | 1 |

Number of external pieces | 20 |

Level of complexity | 6 |

Related polytopes | |

Army | Otwadip |

Regiment | Otwadip |

Dual | Octagonal-dodecagonal duotegum |

Conjugates | Octagonal-dodecagrammic duoprism, Octagrammic-dodecagonal duoprism, Octagrammic-dodecagrammic duoprism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(8)×I_{2}(12), order 384 |

Convex | Yes |

Nature | Tame |

The **octagonal-dodecagonal duoprism** or **otwadip**, also known as the **8-12 duoprism**, is a uniform duoprism that consists of 8 dodecagonal prisms and 12 octagonal prisms, with two of each joining at each vertex.

This polychoron can be alternated into a square-hexagonal duoantiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a hexagonal-square prismantiprismoid or the dodecagons into long ditrigons to create a square-hexagonal prismantiprismoid, or it can be subsymmetrically faceted into a digonal-triangular tetraswirlprism, which are nonuniform.

## Vertex coordinates[edit | edit source]

The coordinates of an octagonal-dodecagonal duoprism of edge length 1, centered at the origin, are given by:

## Representations[edit | edit source]

An octagonal-dodecagonal duoprism has the fllowing Coxeter diagrams:

- x8o x12o (full symmetry)
- x4x x12o (octagons as ditetragons)
- x6x x8o (dodecagons as dihexagons)
- x4x x6x (both of these applied)

## External links[edit | edit source]

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

- Klitzing, Richard. "otwadip".