Helix

From Polytope Wiki
(Redirected from Helices)
Jump to navigation Jump to search
Helix
Rank2
Notation
Schläfli symbol
Elements
Edges
Vertices
Vertex figureLine segment, < edge length < 2
Related polytopes
DualHelix
Abstract & topological properties
Flag count
Schläfli type{∞}
OrientableYes
Properties
ConvexNo
Net count1
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]

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[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]