# Pentagonal-hexagonal duoprismatic prism

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Pentagonal-hexagonal duoprismatic prism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Pehip |

Coxeter diagram | x x5o x6o |

Elements | |

Tera | 6 square-pentagonal duoprisms, 5 square-hexagonal duoprisms, 2 pentagonal-hexagonal duoprisms |

Cells | 30 cubes,5+10 hexagonal prisms, 6+12 pentagonal prisms |

Faces | 30+30+60 squares, 10 hexagons, 12 pentagons |

Edges | 30+60+60 |

Vertices | 60 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Squipdip–pip–squipdip: 120° |

Shiddip–hip–shiddip: 108° | |

Shiddip–cube–squipdip: 90° | |

Phiddip–pip–squipdip: 90° | |

Shiddip–hip–phiddip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 13 |

Level of complexity | 30 |

Related polytopes | |

Army | Pehip |

Regiment | Pehip |

Dual | Pentagonal-hexagonal duotegmatic tegum |

Conjugate | Pentagrammic-hexagonal duoprismatic prism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | H_{2}×G_{2}×A_{1}, order 240 |

Convex | Yes |

Nature | Tame |

The **pentagonal-hexagonal duoprismatic prism** or **pehip**, also known as the **pentagonal-hexagonal prismatic duoprism**, is a convex uniform duoprism that consists of 2 pentagonal-hexagonal duoprisms, 5 square-hexagonal duoprisms, and 6 square-pentagonal duoprisms. Each vertex joins 2 square-pentagonal duoprisms, 2 square-hexagonal duoprisms, and 1 pentagonal-hexagonal 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-hexagonal duoprismatic prism of edge length 1 are given by:

## Representations[edit | edit source]

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

- x x5o x6o (full symmetry)
- x x5o x3x (hexagons as ditrigons)
- xx5oo xx6oo&#x (pentagonal-hexagonal duoprism atop pentagonal-hexagonal duoprism)
- xx5oo xx3xx&#x