# Pentagonal antiditetragoltriate

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Pentagonal antiditetragoltriate | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Notation | |

Bowers style acronym | Paddet |

Elements | |

Cells | 25+25 tetragonal disphenoids, 50 rectangular pyramids, 10 pentagonal prisms |

Faces | 100+100 isosceles triangles, 50 rectangles, 10 pentagons |

Edges | 50+50+100 |

Vertices | 50 |

Vertex figure | Biaugmented triangular prism |

Measures (based on same duoprisms as optimized pentagonal ditetragoltriate) | |

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

Lacing edges (50): | |

Edges of larger pentagon (50): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Paddet |

Regiment | Paddet |

Dual | Pentagonal antitetrambitriate |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | h_{2}≀S_{2}, order 200 |

Convex | Yes |

Nature | Tame |

The **pentagonal antiditetragoltriate** or **paddet** is a convex isogonal polychoron and the third member of the antiditetragoltriate family. It consists of 10 pentagonal prisms, 50 rectangular pyramids, and 50 tetragonal disphenoids of two kinds. 2 pentagonal prisms, 4 tetragonal disphenoids, and 5 rectangular pyramids join at each vertex. However, it cannot be made scaliform.

It can be formed as the convex hull of 2 oppositely oriented semi-uniform pentagonal duoprisms where the larger pentagon is more than times the edge length of the smaller one.

The grand antiprism can be thought of as the convex hull of two inversely oriented pentagonal antiditetragoltriates, with the pentagons having a ratio of 1: ≈ 1:1.61803.