# Octagonal antiprism

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Octagonal antiprism | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Oap |

Coxeter diagram | s2s16o |

Conway notation | A8 |

Elements | |

Faces | 16 triangles, 2 octagons |

Edges | 16+16 |

Vertices | 16 |

Vertex figure | Isosceles trapezoid, edge lengths 1, 1, 1, √2+√2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 3–3: |

8–3: | |

Height | |

Central density | 1 |

Number of external pieces | 18 |

Level of complexity | 4 |

Related polytopes | |

Army | Oap |

Regiment | Oap |

Dual | Octagonal antitegum |

Conjugates | Octagrammic antiprism, Octagrammic retroprism |

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 |

The **octagonal antiprism**, or **oap**, is a prismatic uniform polyhedron. It consists of 16 triangles and 2 octagons. Each vertex joins one octagon and three triangles. As the name suggests, it is an antiprism based on an octagon.

## Vertex coordinates[edit | edit source]

An octagonal antiprism of edge length 1 has vertex coordinates given by:

where is the distance between the antiprism's center and the center of one of its bases.

## Representations[edit | edit source]

An octagonal prism can be represented by the following Coxeter diagrams:

- s2s16o (alternated hexadecagonal prism)
- s2s8s (alternated dioctagonal prism)
- xo8ox&#x (bases considered separately)

## Related polyhedra[edit | edit source]

A square cupola can be attached to a base of the octagonal antiprism to form the gyroelongated square cupola. If a second square cupola is attached to the other base, the result is the gyroelongated square bicupola.

## External links[edit | edit source]

- Klitzing, Richard. "oap".
- Quickfur. "The Octagonal Antiprism".

- Wikipedia contributors. "Octagonal antiprism".
- McCooey, David. "Octagonal Antiprism"