# Dodecagonal duotegum

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Dodecagonal duotegum | |
---|---|

Rank | 4 |

Type | Noble |

Notation | |

Bowers style acronym | Twaddit |

Coxeter diagram | m12o2m12o |

Elements | |

Cells | 144 tetragonal disphenoids |

Faces | 288 isosceles triangles |

Edges | 24+144 |

Vertices | 24 |

Vertex figure | Dodecagonal tegum |

Measures (based on dodecagons of edge length 1) | |

Edge lengths | Base (24): 1 |

Lacing (144): | |

Circumradius | |

Inradius | |

Central density | 1 |

Related polytopes | |

Army | Twaddit |

Regiment | Twaddit |

Dual | Dodecagonal duoprism |

Conjugate | Dodecagrammic duotegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

The **dodecagonal duotegum** or **twaddit**, also known as the **dodecagonal-dodecagonal duotegum**, the **12 duotegum**, or the **12-12 duotegum**, is a noble duotegum that consists of 144 tetragonal disphenoids and 24 vertices, with 24 cells joining at each vertex. It is also the 24-11 step prism. It is the first in an infinite family of isogonal dodecagonal hosohedral swirlchora and also the first in an infinite family of isochoric dodecagonal dihedral swirlchora.

## Vertex coordinates[edit | edit source]

The vertices of a dodecagonal duotegum based on 2 dodecagons of edge length 1, centered at the origin, are given by: