# Dodecagonal duoexpandoprism

Dodecagonal duoexpandoprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Notation | |

Bowers style acronym | Twaddep |

Coxeter diagram | xo12xx ox12xx&#zy |

Elements | |

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

Faces | 576 isosceles triangles, 576 isosceles trapezoids, 288+288 rectangles, 48 dodecagons |

Edges | 288+288+576+576 |

Vertices | 576 |

Vertex figure | Mirror-symmetric triangular antiprism |

Measures (based on two dodecagonal-icositetragonal duoprisms of edge length 1) | |

Edge lengths | Edges of duoprisms (288+288+576): 1 |

Lacing edges (576): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Twaddep |

Regiment | Twaddep |

Dual | Dodecagonal duoexpandotegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

The **dodecagonal duoexpandoprism** or **twaddep** is a convex isogonal polychoron and the eleventh member of the duoexpandoprism family. It consists of 48 dodecagonal prisms of two kinds, 144 rectangular trapezoprisms, 288 wedges, and 144 tetragonal disphenoids. 2 dodecagonal prisms, 1 tetragonal disphenoid, 3 wedges, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal dodecagonal-icositetragonal duoprisms, or more generaly dodecagonal-didodecagonal duoprisms, and a subset of its variations can be formed by expanding the cells of the dodecagonal duoprism outward. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.48709.