# Octagonal-great rhombicuboctahedral duoprism

Octagonal-great rhombicuboctahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Ogirco |

Coxeter diagram | x8o x4x3x () |

Elements | |

Tera | 12 square-octagonal duoprisms, 8 hexagonal-octagonal duoprisms, 6 octagonal duoprisms, 8 great rhombicuboctahedral prisms |

Cells | 96 cubes, 64 hexagonal prisms, 24+24+24+48 octagonal prisms, 8 great rhombicuboctahedra |

Faces | 96+192+192+192 squares, 64 hexagons, 48+48 octagons |

Edges | 192+192+192+384 |

Vertices | 384 |

Vertex figure | Mirror-symmetric pentachoron, edge lengths √2, √3, √2+√2 (base triangle), √2+√2 (top edge), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Sodip–op–hodip: |

Sodip–op–odip: 135° | |

Gircope–girco–gircope: 135° | |

Hodip–op–odip: | |

Sodip–cube–gircope: 90° | |

Hodip–hip–gircope: 90° | |

Odip–op–gircope: 90° | |

Central density | 1 |

Number of external pieces | 34 |

Level of complexity | 60 |

Related polytopes | |

Army | Ogirco |

Regiment | Ogirco |

Dual | Octagonal-disdyakis dodecahedral duotegum |

Conjugate | Octagrammic-quasitruncated cuboctahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

The **octagonal-great rhombicuboctahedral duoprism** or **ogirco** is a convex uniform duoprism that consists of 8 great rhombicuboctahedral prisms, 6 octagonal duoprisms, 8 hexagonal-octagonal duoprisms, and 12 square-octagonal duoprisms. Each vertex joins 2 great rhombicuboctahedral prisms, 1 square-octagonal duoprism, 1 hexagonal-octagonal duoprism, and 1 octagonal duoprism.

The octagonal-great rhombicuboctahedral duoprism can be vertex-inscribed into the cellirhombated penteractitriacontaditeron.

This polyteron can be alternated into a square-snub cubic duoantiprism, although it cannot be made uniform. The octagons can also be edge-snubbed to create a snub cubic-square prismantiprismoid or the great rhombicuboctahedra to create a square-pyritohedral prismantiprismoid, which are also both nonuniform.

## Vertex coordinates[edit | edit source]

The vertices of an octagonal-great rhombicuboctahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:

## Representations[edit | edit source]

An octagonal-great rhombicuboctahedral duoprism has the following Coxeter diagrams:

- x8o x4x3x (full symmetry)
- x4x x4x3x () (BC
_{3}×BC_{2}symmetry, octagons as ditetragons)

## External links[edit | edit source]

- Klitzing, Richard. "ogirco".