# Pentagonal-hexagonal duoprism

Jump to navigation
Jump to search

Pentagonal-hexagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Phiddip |

Coxeter diagram | x5o2x6o () |

Elements | |

Cells | 6 pentagonal prisms, 5 hexagonal prisms |

Faces | 30 squares, 6 pentagons, 5 hexagons |

Edges | 30+30 |

Vertices | 30 |

Vertex figure | Digonal disphenoid, edge lengths (1+√5)/2 (base 1), √3 (base 2), and √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Pip–5–pip: 120° |

Hip–6–hip: 108° | |

Hip–4–pip: 90° | |

Central density | 1 |

Number of external pieces | 11 |

Level of complexity | 6 |

Related polytopes | |

Army | Phiddip |

Regiment | Phiddip |

Dual | Pentagonal-hexagonal duotegum |

Conjugate | Pentagrammic-hexagonal duoprism |

Abstract & topological properties | |

Flag count | 720 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{2}×G_{2}, order 120 |

Flag orbits | 6 |

Convex | Yes |

Nature | Tame |

The **pentagonal-hexagonal duoprism** or **phiddip**, also known as the **5-6 duoprism**, is a uniform duoprism that consists of 5 hexagonal prisms and 6 pentagonal prisms, with two of each joining at each vertex.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a pentagonal-hexagonal duoprism with edge length 1 are given by:

- ,
- ,
- ,
- ,
- ,
- .

## Representations[edit | edit source]

A pentagonal-hexagonal duoprism has the following Coxeter diagrams:

- x5o2x6o () (full symmetry)
- x3x2x5o () (A
_{2}×H_{2}symmetry, hexagons as ditrigons) - ofx xxx6ooo&#xt (G
_{2}×A_{1}axial) - ofx xxx3xxx&#xt (A
_{2}×A_{1}symmetry, ditrigonal axial) - xux xxx5ooo&#xt (H
_{2}×A_{1}axial)

## External links[edit | edit source]

- Bowers, Jonathan. "Category A: Duoprisms".

- Klitzing, Richard. "phiddip".