Helix

Helix
Rank	2
Dimension	3
Type	Regular
Notation
Schläfli symbol	$\{\infty \}\#\{n\}$
Elements
Edges	$N$
Vertices	$N$
Vertex figure	Line segment, $2\sin \left({\frac {\pi (n-2)}{2n}}\right)$ < edge length < 2
Related polytopes
Dual	Helix
Abstract & topological properties
Flag count	$2N$
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

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.

External links

• Wikipedia contributors. "Infinite skew polygon".