# Octagonal-tetrahedral duoprism

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

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Otet |

Coxeter diagram | x8o x3o3o () |

Elements | |

Tera | 8 tetrahedral prisms, 4 triangular-octagonal duoprisms |

Cells | 8 tetrahedra, 32 triangular prisms, 6 octagonal prisms |

Faces | 32 triangles, 48 squares, 4 octagons |

Edges | 32+48 |

Vertices | 32 |

Vertex figure | Triangular scalene, edge lengths 1 (base triangle), √2+√2 (top), √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tepe–tet–tepe: 135° |

Tepe–trip–todip: 90° | |

Todip–op–todip: | |

Heights | Oc atop todip: |

Op atop perp op: | |

Central density | 1 |

Number of external pieces | 12 |

Level of complexity | 10 |

Related polytopes | |

Army | Otet |

Regiment | Otet |

Dual | Octagonal-tetrahedral duotegum |

Conjugate | Octagrammic-tetrahedral duoprism |

Abstract & topological properties | |

Flag count | 3840 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}×I_{2}(8), order 384 |

Convex | Yes |

Nature | Tame |

The **octagonal-tetrahedral duoprism** or **otet** is a convex uniform duoprism that consists of 8 tetrahedral prisms and 4 triangular-octagonal duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular-octagonal duoprisms.

## Vertex coordinates[edit | edit source]

The vertices of an octagonal-tetrahedral duoprism of edge length 1 are given by all even sign changes of the last three coordinates of:

## Representations[edit | edit source]

An octagonal-tetrahedral duoprism has the following Coxeter diagrams:

- x8o x3o3o (full symmetry)
- x4x x3o3o (octagons as ditetragons)
- ox3oo xx8oo&#x (octagon atop triangular-octagonal duoprism)
- ox xo xx8oo&#x (octagonal prism atop orthogonal octagonal prism)

## External links[edit | edit source]

- Klitzing, Richard. "otet".