# Octagonal antitegum

The **octagonal antitegum**, also known as the **octagonal trapezohedron**, is an antitegum based on the octagon, constructed as the dual of an octagonal antiprism. It has 16 kites as faces, with 2 order–8 and 16 order–3 vertices.

Octagonal antitegum | |
---|---|

Rank | 3 |

Type | Uniform dual |

Notation | |

Bowers style acronym | Oat |

Coxeter diagram | p2p16o () |

Conway notation | dA8 |

Elements | |

Faces | 16 kites |

Edges | 16+16 |

Vertices | 2+16 |

Vertex figure | 2 octagons, 16 triangles |

Measures (edge length 1) | |

Dihedral angle | |

Central density | 1 |

Number of external pieces | 16 |

Level of complexity | 4 |

Related polytopes | |

Army | Oat |

Regiment | Oat |

Dual | Octagonal antiprism |

Conjugates | Octagrammic antitegum, Octagrammic concave antitegum |

Abstract & topological properties | |

Flag count | 128 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | (I_{2}(16)×A_{1})/2, order 32 |

Convex | Yes |

Nature | Tame |

Each face of this polyhedron is a kite with its longer edges times the length of its shorter edges.

## External links edit

- Wikipedia contributors. "Octagonal trapezohedron".
- McCooey, David. "Octagonal Trapezohedron"