# Octagonal-snub cubic duoprism

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

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Osnic |

Coxeter diagram | x8o s4s3s |

Elements | |

Tera | 8+24 triangular-octagonal duoprisms, 6 square-octagonal duoprismss, 8 snub cubic prisms |

Cells | 64+192 triangular prisms, 48 cubes, 12+24+24 octagonal prisms, 8 snub cubes |

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

Edges | 96+192+192+192 |

Vertices | 192 |

Vertex figure | Mirror-symmetric pentagonal scalene, edge lengths 1, 1, 1, 1, √2 (base pentagon), √2+√2 (top edge), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | ≈ 1.87421 |

Hypervolume | ≈ 38.09378 |

Diteral angles | Todip–op–todip: ≈ 153.23459° |

Todip–op–sodip: ≈ 142.98343° | |

Sniccup–snic–sniccup: 135° | |

Todip–trip–sniccup: 90° | |

Sodip–cube–sniccup: 90° | |

Central density | 1 |

Number of external pieces | 46 |

Level of complexity | 50 |

Related polytopes | |

Army | Osnic |

Regiment | Osnic |

Dual | Octagonal-pentagonal icositetrahedral duotegum |

Conjugate | Octagrammic-snub cubic duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}+×I2(8), order 384 |

Convex | Yes |

Nature | Tame |

The **octagonal-snub cubic duoprism** or **osnic** is a convex uniform duoprism that consists of 8 snub cubic prisms, 6 square-octagonal duoprisms, and 32 triangular-octagonal duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-octagonal duoprisms, and 1 square-octagonal duoprism.

## Vertex coordinates[edit | edit source]

The vertices of a octagonal-snub cubic duoprism of edge length 1 are given by by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes, of the last three coordinates of:

where