# Decagonal ditetragoltriate

Decagonal ditetragoltriate | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Dedet |

Elements | |

Cells | 100 rectangular trapezoprisms, 20 decagonal prisms |

Faces | 200 isosceles trapezoids, 200 rectangles, 20 decagons |

Edges | 100+200+200 |

Vertices | 200 |

Vertex figure | Notch |

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

Edge lengths | Edges of smaller decagon (200): 1 |

Lacing edges (100): 1 | |

Edges of longer decagon (200): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Dedet |

Regiment | Dedet |

Dual | Decagonal tetrambitriate |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(10)≀S_{2}, order 800 |

Convex | Yes |

Nature | Tame |

The **decagonal ditetragoltriate** or **dedet** is a convex isogonal polychoron and the eighth member of the ditetragoltriate family. It consists of 20 decagonal prisms and 100 rectangular trapezoprisms. 2 decagonal 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 decagonal prismatic swirlchora.

This polychoron can be alternated into the grand antiprism, which can be made uniform.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.43702. This value is also the ratio between the two sides of the two semi-uniform duoprisms.