# Octagonal duoprism

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

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Odip |

Coxeter diagram | x8o x8o () |

Elements | |

Cells | 16 octagonal prisms |

Faces | 64 squares, 16 octagons |

Edges | 128 |

Vertices | 64 |

Vertex figure | Tetragonal disphenoid, edge lengths √2+√2 (bases) and √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dichoral angles | Op–8–op: 135° |

Op–4–op: 90° | |

Central density | 1 |

Number of external pieces | 16 |

Level of complexity | 3 |

Related polytopes | |

Army | Odip |

Regiment | Odip |

Dual | Octagonal duotegum |

Conjugate | Octagrammic duoprism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(8)≀S_{2}, order 512 |

Convex | Yes |

Nature | Tame |

The **octagonal duoprism** or **odip**, also known as the **octagonal-octagonal duoprism**, the **8 duoprism** or the **8-8 duoprism**, is a noble uniform duoprism that consists of 16 octagonal prisms, with 4 joining at each vertex. It is also the digonal double gyrotrapezohedroid and the 16-7 gyrochoron. It is the first in an infinite family of isogonal octagonal dihedral swirlchora, the first in an infinite family of isochoric octagonal hosohedral swirlchora and also the first in an infinite family of isochoric digonal tegmatic swirlchora.

The octagonal duoprism can be vertex-inscribed into a small rhombated tesseract or small prismatotetracontoctachoron.

This polychoron can be alternated into a square duoantiprism, although it cannot be made uniform. Eight of the octagons can also be alternated into long rectangles to create a square-square prismantiprismoid, which is also nonuniform.

It can form a non-Wythoffian uniform hyperbolic tiling with 288 octagonal duoprisms at each vertex with a bitetracontoctachoron as the vertex figure, called an octagonal duoprismatic tetracomb.

## Gallery[edit | edit source]

Wireframe, cell, net

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of an octagonal duoprism of edge length 1, centered at the origin, are given by:

## Representations[edit | edit source]

An octagonal duoprism has the following Coxeter diagrams:

- x8o x8o (full symmetry)
- x4x x8o (BC2×I2(8) symmetry)
- x4x x4x (BC2×BC2 symmetry, both octagons as ditetragons)
- xwwx xxxx4xxxx&#xt (BC2×A1 axial, octagonal prism-first)

## Related polychora[edit | edit source]

Non-adjacent cells of the octagonal duoprism can be augmented with square pucofastegiums. If 8 cells are augmented in this way, so that all the cupolas blend with the prisms into small rhombicuboctahedra, the result is the uniform small rhombated tesseract.

An octagonal duoprism of edge length 1 contains the vertices of a hexadecachoron of edge length , since the hexadecachoron is the 8-3 step prism.

## External links[edit | edit source]

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

- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".

- Klitzing, Richard. "odip".

- Wikipedia Contributors. "8-8 duoprism".