# Zigzag

Zigzag | |
---|---|

Rank | 2 |

Type | Regular |

Space | Euclidean |

Notation | |

Schläfli symbol | |

Elements | |

Edges | |

Vertices | |

Vertex figure | Line segment, 0 < edge length < 2 |

Related polytopes | |

Dual | Zigzag |

Topological properties | |

Orientable | Yes |

Properties | |

Convex | No |

A **zigzag** is a regular apeirogon whose vertices are co-planar but not co-linear. It may be considered a skew polygon even though it is co-planar.

## As a Petrie polygon[edit | edit source]

Zigzags appear as Petrie polygons of several polyhedra, in particular in Euclidean tilings, such as the triangular tiling, square tiling, and the hexagonal tiling. As a result they appear as faces of the Petrie duals of these polyhedra: the Petrial triangular tiling, Petrial square tiling, and Petrial hexagonal tiling.

The zigzag also appears as a Petrie polygons in polyhedra made by gyroelongating along an apeirogon. For example a zigzag is one of the Petrie polygons of the apeirogonal antiprism (a gyroelongation of the apeirogonal dihedron). The zigzag then also appears as a face of their Petrie duals.

## Related polygons[edit | edit source]

### Truncated zigzags[edit | edit source]

There are truncated zigzags which are uniform but not regular formed by truncating or quasitruncating the zigzag.

### Regular skew polygons[edit | edit source]

Just as the flat apeirogon can be viewed as the limit of regular n-gons as n goes to infinity, the zigzag can be viewed as the limit of regular skew n-gons as n goes to infinity. This results in the zigzag often being classified as a skew polygon despite it being planar.

## External Resources[edit | edit source]

- Wikipedia Contributors. "Infinite skew polygon".