# Pentagonal ditetragoltriate

Pentagonal ditetragoltriate | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Notation | |

Bowers style acronym | Pedet |

Elements | |

Cells | 25 rectangular trapezoprisms, 10 pentagonal prisms |

Faces | 50 isosceles trapezoids, 50 rectangles, 10 pentagons |

Edges | 25+50+50 |

Vertices | 50 |

Vertex figure | Notch |

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

Edge lengths | Edges of smaller pentagon (50): 1 |

Lacing edges (25): 1 | |

Edges of larger pentagon (50): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Pedet |

Regiment | Pedet |

Dual | Pentagonal tetrambitriate |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{2}≀S_{2}, order 200 |

Convex | Yes |

Nature | Tame |

The **pentagonal ditetragoltriate** or **pedet** is a convex isogonal polychoron and the third member of the ditetragoltriate family. It consists of 10 pentagonal prisms and 25 rectangular trapezoprisms. 2 pentagonal 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 pentagonal prismatic swirlchora.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.83125. This value is also the ratio between the two sides of the two semi-uniform duoprisms.