# Octagonal ditetragoltriate

Octagonal ditetragoltriate | |
---|---|

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 |

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.

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 | edit source]

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