# Decagonal duoprismatic prism

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

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Daddip |

Coxeter diagram | x x10o x10o () |

Elements | |

Tera | 20 square-decagonal duoprisms, 2 decagonal duoprisms |

Cells | 100 cubes, 20+40 decagonal prisms |

Faces | 200+200 squares, 40 decagons |

Edges | 100+400 |

Vertices | 200 |

Vertex figure | Tetragonal disphenoidal pyramid, edge lengths √(5+√5)/2 (disphenoid bases) and √2 (remaining edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Squadedip–dip–squadedip: 144° |

Squadedip–cube–squadedip: 90° | |

Dedip–dip–squadedip: 90° | |

Height | Dedip atop dedip: 1 |

Central density | 1 |

Number of external pieces | 22 |

Level of complexity | 15 |

Related polytopes | |

Army | Daddip |

Regiment | Daddip |

Dual | Decagonal duotegmatic tegum |

Conjugate | Decagrammic duoprismatic prism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(10)≀S_{2}×A_{1}, order 1600 |

Convex | Yes |

Nature | Tame |

The **decagonal duoprismatic prism** or **daddip**, also known as the **decagonal-decagonal prismatic duoprism**, is a convex uniform duoprism that consists of 2 decagonal duoprisms and 20 square-decagonal duoprisms. Each vertex joins 4 square-decagonal duoprisms and 1 decagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

This polyteron can be alternated into a pentagonal duoantiprismatic antiprism, although it cannot be made uniform.

## Vertex coordinates[edit | edit source]

The vertices of an decagonal duoprismatic prism of edge length 2sin(π/9) are given by:

## Representations[edit | edit source]

A decagonal duoprismatic prism has the following Coxeter diagrams:

- x x10o x10o () (full symmetry)
- x x5x x5x () (decagons as dipentagons)
- xx10oo xx10oo&#x (decagonal duoprism atop decagonal duoprism)
- xx5xx xx5xx&#x