# Octagonal-decagonal duoprism

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Octagonal-decagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Odedip |

Coxeter diagram | x8o x10o () |

Elements | |

Cells | 10 octagonal prisms, 8 decagonal prisms |

Faces | 80 squares, 10 octagons, 8 decagons |

Edges | 80+80 |

Vertices | 80 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Op–8–op: 144° |

Dip–10–dip: 135° | |

Dip–4–op: 90° | |

Central density | 1 |

Number of external pieces | 18 |

Level of complexity | 6 |

Related polytopes | |

Army | Odedip |

Regiment | Odedip |

Dual | Octagonal-decagonal duotegum |

Conjugates | Octagonal-decagrammic duoprism, Octagrammic-decagonal duoprism, Octagrammic-decagrammic duoprism |

Abstract & topological properties | |

Flag count | 1920 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(8)×I_{2}(10), order 320 |

Flag orbits | 6 |

Convex | Yes |

Nature | Tame |

The **octagonal-decagonal duoprism** or **odedip**, also known as the **8-10 duoprism**, is a uniform duoprism that consists of 8 decagonal prisms and 10 octagonal prisms, with two of each joining at each vertex.

This polychoron can be alternated into a square-pentagonal duoantiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a pentagonal-square prismantiprismoid, which is also nonuniform.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of an octagonal-decagonal duoprism of edge length 1, centered at the origin, are given by:

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

## Representations[edit | edit source]

An octagonal-decagonal duoprism has the following Coxeter diagrams:

- x8o x10o () (full symmetry)
- x4x x10o () (B
_{2}×I_{2}(10) symmetry, octagons as ditetragons) - x5x x8o () (H
_{2}×I_{2}(8) symmetry, decagons as dipentagons) - x4x x5x () (B
_{2}×H_{2}symmetry, both of these applied)

## External links[edit | edit source]

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

- Klitzing, Richard. "odedip".