# Octagonal-cubic duoprism

Octagonal-cubic duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Ocube |

Coxeter diagram | x8o x4o3o |

Elements | |

Tera | 8 tesseracts, 6 square-octagonal duoprisms |

Cells | 8+48 cubes, 12 octagonal prisms |

Faces | 48+96 squares, 8 octagons |

Edges | 64+96 |

Vertices | 64 |

Vertex figure | Triangular scalene, edge lengths √2+√2 (top), √2 (base triangle and sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tes–cube–tes: 135° |

Tes–cube–sodip: 90° | |

Sodip–op–sodip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 14 |

Level of complexity | 10 |

Related polytopes | |

Army | Ocube |

Regiment | Ocube |

Dual | Octagonal-octahedral duotegum |

Conjugate | Octagrammic-cubic duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I_{2}(8), order 768 |

Convex | Yes |

Nature | Tame |

The **octagonal-cubic duoprism** or **ocube**, also known as a **square-octagonal duoprismatic prism**, is a convex uniform duoprism that consists of 8 tesseracts and 6 square-octagonal duoprisms. Each vertex joins 2 tesseracts and 3 square-octagonal duoprisms. It is a duoprism based on a square and an octagonal prism, which makes it a convex segmentoteron.

This polyteron can be alternated into a square-tetrahedral duoantiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a tetrahedral-square prismantiprismoid, which is also nonuniform.

The octagonal-cubic duoprism can be vertex-inscribed into the small cellated penteractitriacontaditeron.

## Vertex coordinates[edit | edit source]

The vertices of an octagonal-cubic duoprism of edge length 1 are given by:

## Representations[edit | edit source]

An octagonal-cubic duoprism has the following Coxeter diagrams:

- x8o x4o3o (full symmetry)
- x4x x4o3o (octagons as ditetragons)
- x x4o x8o (square-octagonal duoprismatic prism)
- x x4o x4x
- x x x x8o (octagonal prismatic prismatic prism)
- x x x x4x

## External links[edit | edit source]

- Klitzing, Richard. "ocube".