# Octagonal-decagonal duoprismatic prism

Octagonal-decagonal duoprismatic prism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Oddip |

Coxeter diagram | x x8o x10o () |

Elements | |

Tera | 10 square-octagonal duoprisms, 8 square-decagonal duoprisms, 2 octagonal-decagonal duoprisms |

Cells | 80 cubes, 8+16 decagonal prisms, 10+20 octagonal prisms |

Faces | 80+80+160 squares, 20 octagons, 16 decagons |

Edges | 80+160+160 |

Vertices | 160 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Sodip–op–sodip: 144° |

Squadedip–dip–squadedip: 135° | |

Squadedip–cube–sodip: 90° | |

Odedip–op–sodip: 90° | |

Squadedip–dip–odedip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 20 |

Level of complexity | 30 |

Related polytopes | |

Army | Oddip |

Regiment | Oddip |

Dual | Octagonal-decagonal duotegmatic tegum |

Conjugates | Octagonal-decagrammic duoprismatic prism, Octagrammic-decagonal duoprismatic prism, Octagrammic-decagrammic duoprismatic prism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(8)×I_{2}(10)×A_{1}, order 640 |

Convex | Yes |

Nature | Tame |

The **octagonal-decagonal duoprismatic prism** or **oddip**, also known as the **octagonal-decagonal prismatic duoprism**, is a convex uniform duoprism that consists of 2 octagonal-decagonal duoprisms, 8 square-decagonal duoprisms, and 10 square-octagonal duoprisms. Each vertex joins 2 square-octagonal duoprisms, 2 square-decagonal duoprisms, and 1 octagonal-decagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

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

## Vertex coordinates[edit | edit source]

The vertices of an octagonal-decagonal duoprismatic prism of edge length 1 are given by all permutations of the first two coordinates of:

## Representations[edit | edit source]

An octagonal-decagonal duoprismatic prism has the following Coxeter diagrams:

- x x8o x10o (full symmetry)
- x x4x x10o () (BC
_{2}×I_{2}(10)×A_{1}symmetry, octagons as ditetragons) - x x8o x5x () (H
_{2}×I_{2}(8)×A_{1}symmetry, decagons as dipentagons) - x x4x x5x () (BC
_{2}×H_{2}×A_{1}symmetry) - xx8oo xx10oo&#x (octagonal-decagonal duoprism atop octagonal-decagonal duoprism)
- xx4xx xx10oo&#x
- xx8oo xx5xx&#x
- xx4xx xx5xx&#x