# Helix

Helix
Rank2
SpaceSpherical
Notation
Schläfli symbol${\displaystyle \{\infty\}\#\{n\}}$
Elements
Edges${\displaystyle N}$
Vertices${\displaystyle N}$
Vertex figureLine segment, ${\displaystyle 2\sin\left(\frac{\pi(n-2)}{2n}\right)}$ < edge length < 2
Related polytopes
DualHelix
Abstract & topological properties
Flag count${\displaystyle 2N}$
Schläfli type{∞}
OrientableYes
Properties
ConvexNo
Net count1

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

A triangular helix (highlighted in red) as the Petrie polygon of the muoctahedron.

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

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

### Zigzags

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