# Dodecagonal-cubic duoprism

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

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Twacube |

Coxeter diagram | x12o x4o3o () |

Elements | |

Tera | 12 tesseracts, 6 square-dodecagonal duoprisms |

Cells | 12+72 cubes, 12 dodecagonal prisms |

Faces | 72+144 squares, 8 dodecagons |

Edges | 96+144 |

Vertices | 96 |

Vertex figure | Triangular scalene, edge lengths √2+√3 (top), √2 (base triangle and sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tes–cube–tes: 150° |

Tes–cube–sitwadip: 90° | |

Sitwadip–twip–sitwadip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 18 |

Level of complexity | 10 |

Related polytopes | |

Army | Twacube |

Regiment | Twacube |

Dual | Dodecagonal-octahedral duotegum |

Conjugate | Dodecagrammic-cubic duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I2(12), order 1152 |

Convex | Yes |

Nature | Tame |

The **dodecagonal-cubic duoprism** or **twacube**, also known as the **square-dodecagonal duoprismatic prism**, is a convex uniform duoprism that consists of 12 tesseracts and 6 square-dodecagonal duoprisms. Each vertex joins 2 tesseracts and 3 square-dodecagonal duoprisms. It is a duoprism based on a square and a dodecagonal prism, which makes it a convex segmentoteron.

This polyteron can be alternated into a hexagonal-tetrahedral duoantiprism, although it cannot be made uniform. The dodecagons can also be alternated into long ditrigons to create a tetrahedral-hexagonal prismantiprismoid, which is also nonuniform.

## Vertex coordinates[edit | edit source]

The vertices of a dodecagonal-cubic duoprism of edge length 1 are given by:

## Representations[edit | edit source]

A dodecagonal-cubic duoprism has the following Coxeter diagrams:

- x12o x4o3o () (full symmetry)
- x x4o x12o () (square-dodecagonal duoprismatic prism)
- x x x x12o () (dodecagonal prismatic prismatic prism)

## External links[edit | edit source]

- Klitzing, Richard. "twacube".