# Enneagonal ditetragoltriate

Enneagonal ditetragoltriate | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Edet |

Elements | |

Cells | 81 rectangular trapezoprisms, 18 enneagonal prisms |

Faces | 162 isosceles trapezoids, 162 rectangles, 18 enneagons |

Edges | 81+162+162 |

Vertices | 162 |

Vertex figure | Notch |

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

Edge lengths | Edges of smaller enneagon (162): 1 |

Lacing edges (81): 1 | |

Edges of larger enneagon (162): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Edet |

Regiment | Edet |

Dual | Enneagonal tetrambitriate |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(9)≀S_{2}, order 648 |

Convex | Yes |

Nature | Tame |

The **enneagonal ditetragoltriate** or **edet** is a convex isogonal polychoron and the seventh member of the ditetragoltriate family. It consists of 18 enneagonal prisms and 81 rectangular trapezoprisms. 2 enneagonal 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 enneagonal prismatic swirlchora.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.48369. This value is also the ratio between the two sides of the two semi-uniform duoprisms.