# Decagonal-dodecagonal duoprismatic prism

Decagonal-dodecagonal duoprismatic prism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Datwip |

Coxeter diagram | x x10o x12o () |

Elements | |

Tera | 12 square-decagonal duoprisms, 10 square-dodecagonal duoprisms, 2 decagonal-dodecagonal duoprisms |

Cells | 120 cubes, 10+20 dodecagonal prisms, 12+24 decagonal prisms |

Faces | 120+120+240 squares, 24 decagons, 20 dodecagons |

Edges | 120+240+240 |

Vertices | 240 |

Vertex figure | Digonal disphenoidal pyramid, edge lengths √(5+√5)/2 (disphenoid base 1), √2+√3 (disphenoid base 2), √2 (remaining edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Squadedip–dip–squadedip: 150° |

Sitwadip–twip–sitwadip: 144° | |

Sitwadip–cube–squadedip: 90° | |

Datwadip–dip–squadedip: 90° | |

Sitwadip–twip–datwadip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 24 |

Level of complexity | 30 |

Related polytopes | |

Army | Datwip |

Regiment | Datwip |

Dual | Decagonal-dodecagonal duotegmatic tegum |

Conjugates | Decagonal-dodecagrammic duoprismatic prism, Decagrammic-dodecagonal duoprismatic prism, Decagrammic-dodecagrammic duoprismatic prism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(10)×I_{2}(12)×A_{1}, order 960 |

Convex | Yes |

Nature | Tame |

The **decagonal-dodecagonal duoprismatic prism** or **datwip**, also known as the **decagonal-dodecagonal prismatic duoprism**, is a convex uniform duoprism that consists of 2 decagonal-dodecagonal duoprisms, 10 square-dodecagonal duoprisms, and 12 square-decagonal duoprisms. Each vertex joins 2 square-decagonal duoprisms, 2 square-dodecagonal duoprisms, and 1 decagonal-dodecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

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

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

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

- x x10o x12o () (full symmetry)
- x x5x x12o ()(decagons as dipentagons)
- x x10o x6x ()(dodecagons as dihexagons)
- x x5x x6x ()
- xx10oo xx12oo&#x (decagonal-hendecagonal duoprism atop decagonal-hendecagonal duoprism)
- xx5xx xx12oo&#x
- xx10oo xx6xx&#x
- xx5xx xx6xx&#x