# Pentagrammic-octagonal duoprism

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Pentagrammic-octagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Starodip |

Coxeter diagram | x5/2o x8o() |

Elements | |

Cells | 8 pentagrammic prisms, 5 octagonal prisms |

Faces | 40 squares, 8 pentagrams, 5 octagons |

Edges | 40+40 |

Vertices | 40 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Stip–5/2–stip: 135° |

Stip–4–op: 90° | |

Op–8–op: 36° | |

Central density | 2 |

Number of external pieces | 18 |

Level of complexity | 12 |

Related polytopes | |

Army | Semi-uniform podip |

Regiment | Starodip |

Dual | Pentagrammic-octagonal duotegum |

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

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

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

Convex | No |

Nature | Tame |

The **pentagrammic-octagonal duoprism**, also known as **starodip** or the **5/2-8 duoprism**, is a uniform duoprism that consists of 8 pentagrammic prisms and 5 octagonal prisms, with 2 of each at each vertex.

## Vertex coordinates[edit | edit source]

The coordinates of a pentagrammic-octagonal duoprism, centered at the origin and with unit edge length, are given by:

## Representations[edit | edit source]

A pentagrammic-octagonal duoprism has the following Coxeter diagrams:

- x5/2o x8o (full symmetry)
- x4x x5/2o () (BC
_{2}×H_{2}symmetry, octagons as ditetragons)

## External links[edit | edit source]

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

- Klitzing, Richard. "starodip".