# Hexagonal ditetragoltriate

Hexagonal ditetragoltriate | |
---|---|

File:Hexagonal ditetragoltriate.png | |

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Hiddet |

Elements | |

Cells | 36 rectangular trapezoprisms, 12 hexagonal prisms |

Faces | 72 isosceles trapezoids, 72 rectangless, 12 hexagons |

Edges | 36+72+72 |

Vertices | 72 |

Vertex figure | Notch |

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

Edge lengths | Edges of smaller hexagon (72): 1 |

Lacing edges (36): 1 | |

Edges of larger hexagon (72): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Hiddet |

Regiment | Hiddet |

Dual | Hexagonal tetrambitriate |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | G_{2}≀S_{2}, order 288 |

Convex | Yes |

Nature | Tame |

The **hexagonal ditetragoltriate** or **hiddet** is a convex isogonal polychoron and the fourth member of the ditetragoltriate family. It consists of 12 hexagonal prisms and 36 rectangular trapezoprisms. 2 hexagonal prisms and 4 rectangular trapeozpirsms join at each vertex. However, it cannot be made uniform. It is the first in an infinite family of isogonal hexagonal prismatic swirlchora.

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

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.70711. This value is also the ratio between the two sides of the two semi-uniform duoprisms.

## Vertex coordinates[edit | edit source]

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