# Dodecagonal antiditetragoltriate

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Dodecagonal antiditetragoltriate | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Notation | |

Bowers style acronym | Twadet |

Elements | |

Cells | 144+144 tetragonal disphenoids, 288 rectangular pyramids, 24 dodecagonal prisms |

Faces | 576+576 isosceles triangles, 288 rectangles, 24 dodecagons |

Edges | 288+288+576 |

Vertices | 288 |

Vertex figure | Biaugmented triangular prism |

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

Edge lengths | Edges of smaller dodecagon (288): 1 |

Lacing edges (576): | |

Edges of larger dodecagon (288): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Twadet |

Regiment | Twadet |

Dual | Dodecagonal antitetrambitriate |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(12)≀S_{2}, order 1152 |

Convex | Yes |

Nature | Tame |

The **dodecagonal antiditetragoltriate** or **twadet** is a convex isogonal polychoron and the tenth member of the antiditetragoltriate family. It consists of 24 dodecagonal prisms, 288 rectangular pyramids, and 288 tetragonal disphenoids of two kinds. 2 dodecagonal prisms, 4 tetragonal dispheonids, and 5 rectangular pyraids join at each vertex. However, it cannot be made scaliform.

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