Skew hexagon

Skew hexagon
Rank	2
Dimension	3
Type	Regular
Notation
Schläfli symbol	$\{6\}\#\{\}$ $\{6\}\#\{2\}$ $\left\{{\dfrac {6}{1,3}}\right\}$
Elements
Edges	6
Vertices	6
Related polytopes
Army	Trap
Dual	Flat hexagon
Convex hull	Triangular antiprism
Abstract & topological properties
Euler characteristic	0
Schläfli type	{6}
Orientable	Yes
Properties
Symmetry	(G2×A1)/2, order 12
Convex	No
Dimension vector	(1,2)

This article is about the hexagon skewed by a digon. For the hexagon skewed by a triangle, see Hexagonal-triangular coil.

The skew hexagon is a regular skew polygon in 3D Euclidean space. It is the result of blending a hexagon with a digon.

Related polytopes

Its edges are the side edges of a triangular antiprism.

The cube and octahedron each have four skew hexagons as Petrie polygons.

Its apeir is the Petrial helical triangular tiling, making it one of 3 polygons in 3 dimensions with a non-dense apeir.

Other skew hexagons

The skew hexagon is one of five regular hexagons in Euclidean space:

Hexagons in Euclidean space

Name	Extended Schläfli symbol	Dimensions
hexagon	$\left\{{\dfrac {6}{1}}\right\}$	2
hexagonal-triangular coil	$\left\{{\dfrac {6}{1,2}}\right\}$	4
skew hexagon	$\left\{{\dfrac {6}{1,3}}\right\}$	3
skew triangle	$\left\{{\dfrac {6}{2,3}}\right\}$	3
skew hexagonal-triangular coil	$\left\{{\dfrac {6}{1,2,3}}\right\}$	5