# Octagonal-small rhombicuboctahedral duoprism

Octagonal-small rhombicuboctahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Osirco |

Coxeter diagram | x8o x4o3x |

Elements | |

Tera | 8 triangular-octagonal duoprisms, 6+12 square-octagonal duoprisms, 8 small rhombicuboctahedral prisms |

Cells | 64 triangular prisms, 48+96 cubes, 24+24 octagonal prisms, 8 small rhombicuboctahedra |

Faces | 64 triangles, 48+96+192+192 squares, 24 octagons |

Edges | 192+192+192 |

Vertices | 192 |

Vertex figure | Isosceles-trapezoidal scalene, edge lengths 1, √2, √2, √2 (base trapezoid), √2+√2 (top), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Todip–op–sodip: |

Sodip–op–sodip: 135° | |

Sircope–sirco–sircope: 135° | |

Todip–trip–sircope: 90° | |

Sodip–cube–sircope: 90° | |

Central density | 1 |

Number of external pieces | 34 |

Level of complexity | 40 |

Related polytopes | |

Army | Osirco |

Regiment | Osirco |

Dual | Octagonal-deltoidal icositetrahedral duotegum |

Conjugate | Octagrammic-quasirhombicuboctahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

The **octagonal-small rhombicuboctahedral duoprism** or **osirco** is a convex uniform duoprism that consists of 8 small rhombicuboctahedral prisms, 18 square-octagonal duoprisms, of two kinds and 8 triangular-octagonal duoprisms. Each vertex joins 2 small rhombicuboctahedral prisms, 1 triangular-octagonal duoprism, and 3 square-octagonal duoprisms.

The octagonal-small rhombicuboctahedral duoprism can be vertex-inscribed into a small prismated penteract.

This polyteron can be tetrahedrally alternated into a square-truncated tetrahedral duoalterprism, although it cannot be made scaliform. It can also be tetrahedrally edge-snubbed to create a truncated tetrahedral-square prismalterprismoid, which is also not scaliform.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

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

- x8o x4o3x (full symmetry)
- x4x x4o3x (octagons as ditetragons)

## External links[edit | edit source]

- Klitzing, Richard. "osirco".