# Pentagonal-octagonal duoprism

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Pentagonal-octagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Podip |

Coxeter diagram | x5o x8o () |

Elements | |

Cells | 8 pentagonal prisms, 5 octagonal prisms |

Faces | 40 squares, 8 pentagons, 5 octagons |

Edges | 40+40 |

Vertices | 40 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Pip–5–pip: 135° |

Op–8–op: 108° | |

Pip–4–op: 90° | |

Central density | 1 |

Number of external pieces | 13 |

Level of complexity | 6 |

Related polytopes | |

Army | Podip |

Regiment | Podip |

Dual | Pentagonal-octagonal duotegum |

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

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

The **pentagonal-octagonal duoprism** or **podip**, also known as the **5-8 duoprism**, is a uniform duoprism that consists of 5 octagonal prisms and 8 pentagonal prisms, with two of each joining at each vertex.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A pentagonal-octagonal duoprism has the following Coxeter diagrams:

- x5o x8o (full symmetry)
- x4x x5o (octagons as ditetragons)
- ofx xxx8ooo&#xt (octagonal axial)
- ofx xxx4xxx&#xt (ditetragonal axial)

## External links[edit | edit source]

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

- Klitzing, Richard. "podip".