# Pentagonal-octagrammic duoprism

Pentagonal-octagrammic duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Pistodip |

Coxeter diagram | x5o x8/3o () |

Elements | |

Cells | 8 pentagonal prisms, 5 octagrammic prisms |

Faces | 40 squares, 8 pentagons, 5 octagrams |

Edges | 40+40 |

Vertices | 40 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Stop–8/3–stop: 108° |

Pip–4–stop: 90° | |

Pip–5–pip: 45° | |

Central density | 3 |

Number of external pieces | 21 |

Level of complexity | 12 |

Related polytopes | |

Army | Semi-uniform podip |

Regiment | Pistodip |

Dual | Pentagonal-octagrammic duotegum |

Conjugates | Pentagonal-octagonal duoprism, Pentagrammic-octagonal duoprism, Pentagrammic-octagrammic duoprism |

Abstract & topological properties | |

Flag count | 960 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{2}×I_{2}(8), order 160 |

Convex | No |

Nature | Tame |

The **pentagonal-octagrammic duoprism**, also known as **pistodip** or the **5-8/3 duoprism**, is a uniform duoprism that consists of 8 pentagonal prisms and 5 octagrammic prisms, with 2 of each at each vertex.

## Vertex coordinates[edit | edit source]

The coordinates of a pentagonal-octagrammic duoprism, centered at the origin and with edge length 1, are given by:

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

## Representations[edit | edit source]

A pentagonal-octagrammic duoprism has the following Coxeter diagrams:

- x5o x8/3o () (full symmetry)
- x4/3x x5o () (B
_{2}×H_{2}symmetry, octagrams as ditetragrams)

## External links[edit | edit source]

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

- Klitzing, Richard. "pistodip".