# Petrial octahedron

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Petrial octahedron | |
---|---|

Rank | 3 |

Type | Regular polytope |

Space | Spherical |

Notation | |

Schläfli symbol | {6,4}_{3}{3,4} ^{π} |

Elements | |

Faces | 4 skew hexagons |

Edges | 12 |

Vertices | 6 |

Vertex figure | Square (edge length 1) |

Related polytopes | |

Petrie dual | Octahedron |

Convex hull | Octahedron |

Abstract properties | |

Flag count | 48 |

Euler characteristic | -2 |

Schläfli type | {6,4} |

Topological properties | |

Orientable | No |

Genus | 4 |

Properties | |

Symmetry | B3 |

The **Petrial octahedron** is a regular skew polyhedron consisting of 4 skew hexagons. It is the Petrie dual of the octahedron, therefore shares all of its edges and points with the octahedron. The Petrial octahedron has an Euler characteristic of -2.

## Vertex coordinates[edit | edit source]

The vertex coordinates of a Petrial octahedron with unit side length are shared with a regular octahedron, being all permutations of:

- .

## Related polyhedra[edit | edit source]

The rectification of the petrial octahedron is the cubohemioctahedron.

## External links[edit | edit source]

- Wikipedia Contributors. "Petrie dual".
- Hartley, Michael. "{6,4}*48b".