# Dodecagonal duoprism

The **dodecagonal duoprism** or **twaddip**, also known as the **dodecagonal-dodecagonal duoprism**, the **12 duoprism** or the **12-12 duoprism**, is a noble uniform duoprism that consists of 24 dodecagonal prisms, with 4 joining at each vertex. It is also the 24-11 gyrochoron. It is the first in an infinite family of isogonal dodecagonal dihedral swirlchora and also the first in an infinite family of isochoric dodecagonal hosohedral swirlchora.

Dodecagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Twaddip |

Coxeter diagram | x12o x12o () |

Elements | |

Cells | 24 dodecagonal prisms |

Faces | 144 squares, 24 dodecagons |

Edges | 288 |

Vertices | 144 |

Vertex figure | Tetragonal disphenoid, edge lengths (√2+√6)/2 (bases) and √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dichoral angles | Twip–12–twip: 150° |

Twip–4–twip: 90° | |

Central density | 1 |

Number of external pieces | 24 |

Level of complexity | 3 |

Related polytopes | |

Army | Twaddip |

Regiment | Twaddip |

Dual | Dodecagonal duotegum |

Conjugate | Dodecagrammic duoprism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

This polychoron can be alternated into a hexagonal duoantiprism, although it cannot be made uniform. Twelve of the dodecagons can also be alternated into long ditrigons to create a hexagonal-hexagonal prismantiprismoid, or it can be subsymmetrically faceted into a square triswirlprism or a triangular tetraswirlprism, which are nonuniform.

## Vertex coordinatesEdit

The vertices of a dodecagonal duoprism of edge length 1, centered at the origin, are given by:

## VariationsEdit

A dodecagonal duoprism has the following Coxeter diagrams:

- x12o x12o (full symmetry)
- x6x x12o (one dodecagon as dihexagon)
- x6x x6x (both dodecagons as dihexagons)

## External linksEdit

- Bowers, Jonathan. "Category A: Duoprisms".

- Klitzing, Richard. "twaddip".