# Hexagonal-dodecagonal duoprismatic prism

Hexagonal-dodecagonal duoprismatic prism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Hatwip |

Coxeter diagram | x x6o x12o |

Elements | |

Tera | 12 square-hexagonal duoprisms, 6 square-dodecagonal duoprisms, 2 hexagonal-dodecagonal duoprisms |

Cells | 72 cubes, 6+12 dodecagonal prisms, 12+24 hexagonal prisms |

Faces | 72+72+144 squares, 24 hexagons, 12 dodecagons |

Edges | 72+144+144 |

Vertices | 144 |

Vertex figure | Digonal disphenoidal pyramid, edge lengths √3 (disphenoid base 1), √2+√3 (disphenoid base 2), √2 (remaining edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Shiddip–hip–shiddip: 150° |

Sitwadip–twip–sitwadip: 120° | |

Sitwadip–cube–shiddip: 90° | |

Hitwadip–hip–shiddip: 90° | |

Sitwadip–twip–hitwadip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 20 |

Level of complexity | 30 |

Related polytopes | |

Army | Hatwip |

Regiment | Hatwip |

Dual | Hexagonal-dodecagonal duotegmatic tegum |

Conjugate | Hexagonal-dodecagrammic duoprismatic prism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | G_{2}×I_{2}(12)×A_{1}, order 576 |

Convex | Yes |

Nature | Tame |

The **hexagonal-dodecagonal duoprismatic prism** or **hatwip**, also known as the **hexagonal-dodecagonal prismatic duoprism**, is a convex uniform duoprism that consists of 2 hexagonal-dodecagonal duoprisms, 6 square-dodecagonal duoprisms, and 12 square-hexagonal duoprisms. Each vertex joins 2 square-hexagonal duoprisms, 2 square-dodecagonal duoprisms, and 1 hexagonal-dodecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

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

## Vertex coordinates[edit | edit source]

The vertices of a hexagonal-dodecagonal duoprismatic prism of edge length 1 are given by all permutations of the third and fourth coordinates of:

## Representations[edit | edit source]

A hexagonal-dodecagonal duoprismatic prism has the following Coxeter diagrams:

- x x6o x12o (full symmetry)
- x x3x x12o (hexagons as ditrigons)
- x x6o x6x (dodecagons as dihexagons)
- x x3x x6x
- xx6oo xx12oo&#x (hexagonal-dodecagonal duoprism atop hexagonal-dodecagonal duoprism)
- xx3xx xx12oo&#x
- xx6oo xx6xx&#x
- xx3xx xx6xx&#x