# Helix

Helix | |
---|---|

Rank | 2 |

Dimension | 3 |

Type | Regular |

Notation | |

Schläfli symbol | |

Elements | |

Edges | |

Vertices | |

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

Related polytopes | |

Dual | Helix |

Abstract & topological properties | |

Flag count | |

Schläfli type | {∞} |

Orientable | Yes |

Properties | |

Flag orbits | 1 |

Convex | No |

Net count | 1 |

Dimension vector | (1,1) |

A **helix** is a regular skew apeirogon in 3-dimensional Euclidean space. Helices can be constructed by blending a polygon with a planar apeirogon.

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

Helices appear as Petrie polygons of several Euclidean honeycombs, such as the cubic honeycomb and bitruncated cubic honeycomb. They also appear as Petrie polygons in the pure apeirohedra; the mucube, the muoctahedron, and the mutetrahedron.

## As a facet[edit | edit source]

Helices appear as the facets of several regular skew polyhedra. This includes the Petrials of the mucube, muoctahedron, and mutetrahedron, but also the trihelical square tiling and the tetrahelical triangular tiling.

## Related polygons[edit | edit source]

### Zigzags[edit | edit source]

The zigzag is a planar skew apeirogon which can be viewed as a digonal helix.

## External links[edit | edit source]

- Wikipedia contributors. "Infinite skew polygon".