# Octagrammic duoprism

The **octagrammic duoprism** or **stodip**, also known as the **octagrammic-octagrammic duoprism**, the **8/3 duoprism** or the **8/3-8/3 duoprism**, is a noble uniform duoprism that consists of 16 octagrammic prisms, with 4 meeting at each vertex.

Octagrammic duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Stodip |

Coxeter diagram | x8/3o x8/3o () |

Elements | |

Cells | 16 octagrammic prisms |

Faces | 64 squares, 16 octagrams |

Edges | 128 |

Vertices | 64 |

Vertex figure | Tetragonal disphenoid, edge lengths √2–√2 (bases) and √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dichoral angles | Stop–4–stop: 90° |

Stop–8/3–stop: 45° | |

Central density | 9 |

Number of external pieces | 32 |

Level of complexity | 12 |

Related polytopes | |

Army | Odip, edge length |

Regiment | Stodip |

Dual | Octagrammic duotegum |

Conjugate | Octagonal duoprism |

Abstract & topological properties | |

Flag count | 1536 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(8)≀S_{2}, order 512 |

Convex | No |

Nature | Tame |

The octagrammic duoprism can be vertex-inscribed into a sphenoverted tesseractitesseractihexadecachoron or great distetracontoctachoron.

## Vertex coordinates edit

The vertices of an octagrammic duoprism, centered at the origin and with unit edge length, are given by:

- ,
- ,
- ,
- .

## Representations edit

An octagrammic duoprism has the following Coxeter diagrams:

- x8/3o x8/3o ( ) (full symmetry)
- x4/3x x8/3o ( ) (B
_{2}×I_{2}(8) symmetry, some octagrams as ditetragrams) - x4/3x x4/3x ( ) (B
_{2}≀S_{2}symmetry, all octagrams as ditetragrams)

## External links edit

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

- Klitzing, Richard. "stodip".