# Pentagonal-decagonal duoprismatic prism

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Pentagonal-decagonal duoprismatic prism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Peddip |

Coxeter diagram | x x5o x10o |

Elements | |

Tera | 10 square-pentagonal duoprisms, 5 square-decagonal duoprisms, 2 pentagonal-decagonal duoprisms |

Cells | 50 cubes, 5+10 decagonal prisms, 10+20 pentagonal prisms |

Faces | 50+50+100 squares, 20 pentagons, 10 decagons |

Edges | 50+100+100 |

Vertices | 100 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Squipdip–pip–squipdip: 144° |

Squadedip–dip–squadedip: 108° | |

Squadedip–cube–squipdip: 90° | |

Padedip–pip–squipdip: 90° | |

Squadedip–dip–padedip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 17 |

Level of complexity | 30 |

Related polytopes | |

Army | Peddip |

Regiment | Peddip |

Dual | Pentagonal-decagonal duotegmatic tegum |

Conjugate | Pentagrammic-decagrammic duoprismatic prism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | H_{2}×I_{2}(10)×A_{1}, order 400 |

Convex | Yes |

Nature | Tame |

The **pentagonal-decagonal duoprismatic prism** or **peddip**, also known as the **pentagonal-decagonal prismatic duoprism**, is a convex uniform duoprism that consists of 2 pentagonal-decagonal duoprisms, 5 square-decagonal duoprisms, and 10 square-pentagonal duoprisms. Each vertex joins 2 square-pentagonal duoprisms, 2 square-decagonal duoprisms, and 1 pentagonal-decagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

## Vertex coordinates[edit | edit source]

The vertices of a pentagonal-decagonal duoprismatic prism of edge length 1 are given by:

## Representations[edit | edit source]

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

- x x5o x10o (full symmetry)
- x x5o x5x (decagons as dipentagons)
- xx5oo xx10oo&#x (pentagonal-decagonal duoprism atop pentagonal-decagonal duoprism)
- xx5oo xx5xx&#x