# Octagonal duotegum

Octagonal duotegum | |
---|---|

Rank | 4 |

Type | Noble |

Notation | |

Bowers style acronym | Odit |

Coxeter diagram | m8o2m8o () |

Elements | |

Cells | 64 tetragonal disphenoids |

Faces | 128 isosceles triangles |

Edges | 16+64 |

Vertices | 16 |

Vertex figure | Octagonal tegum |

Measures (based on octagons of edge length 1) | |

Edge lengths | Base (16): 1 |

Lacing (64): | |

Circumradius | |

Inradius | |

Central density | 1 |

Related polytopes | |

Army | Odit |

Regiment | Odit |

Dual | Octagonal duoprism |

Conjugate | Octagrammic duotegum |

Abstract & topological properties | |

Flag count | 1536 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

The **octagonal duotegum** or **odit**, also known as the **octagonal-octagonal duotegum**, the **8 duotegum**, or the **8-8 duotegum**, is a noble duotegum that consists of 64 tetragonal disphenoids and 16 vertices, with 16 cells joining at each vertex. It is also the digonal double gyroantiprismoid and the 16-7 step prism. It is the first in an infinite family of isogonal octagonal hosohedral swirlchora, the first in an infinite family of isochoric octagonal dihedral swirlchora and also the first in an infinite family of isogonal digonal prismatic swirlchora.

It is also known as the **digonal double gyroantiprismoid**.

It is one of a number of isogonal polychora that can be obtained as the hull of various arrangements of 2 hexadecachora.

## Vertex coordinates[edit | edit source]

The vertices of an octagonal duotegum based on 2 octagons of edge length 1, centered at the origin, are given by:

- ,
- ,
- ,
- .

## Related polytopes[edit | edit source]

### Related complex polygon[edit | edit source]

The regular complex polygon has 16 vertices in with a real representation in matching the vertex coordinates of the octagonal duotegum. It has 64 2-edges corresponding to the connecting edges of the octagonal duotegum, while the 16 edges connecting the two octagons are not included.

The skeleton of is a biclique, .^{[1]}

## References[edit | edit source]

- ↑ Coxeter (1974:1114)