# Octagonal ditetragoltriate

The **octagonal ditetragoltriate** or **odet** is a convex isogonal polychoron and the sixth member of the ditetragoltriate family. It consists of 16 octagonal prisms and 64 rectangular trapezoprisms. 2 octagonal prisms and 4 rectangular trapezoprisms join at each vertex. However, it cannot be made uniform. It is the first in an infinite family of isogonal octagonal prismatic swirlchora.

Octagonal ditetragoltriate | |
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File:Octagonal ditetragoltriate.png | |

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Odet |

Elements | |

Cells | 64 rectangular trapezoprisms, 16 octagonal prisms |

Faces | 128 isosceles trapezoids, 128 rectangles, 16 octagons |

Edges | 64+128+128 |

Vertices | 128 |

Vertex figure | Notch |

Measures (based on variant with trapezoids with 3 unit edges) | |

Edge lengths | Edges of smaller octagon (128): 1 |

Lacing edges (64): 1 | |

Edges of larger octagon (128): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Odet |

Regiment | Odet |

Dual | Octagonal tetrambitriate |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

This polychoron can be alternated into a square double antiprismoid, which is also nonuniform.

It can be obtained as the convex hull of 2 similarly oriented semi-uniform octagonal duoprisms, one with a larger xy octagon and the other with a larger zw octagon.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.54120. This value is also the ratio between the two sides of the two semi-uniform duoprisms.

## Vertex coordinates edit

The vertices of an octagonal ditetragoltriate, assuming that the trapezoids have three equal edges of length 1, centered at the origin, are given by: