# Skew hexagon

Skew hexagon
Rank2
Dimension3
TypeRegular
Notation
Schläfli symbol${\displaystyle \{6\}\#\{\}}$
${\displaystyle \{6\}\#\{2\}}$
${\displaystyle \left\{{\dfrac {6}{1,3}}\right\}}$
Elements
Edges6
Vertices6
Related polytopes
ArmyTrap
DualFlat hexagon
Convex hullTriangular antiprism
Abstract & topological properties
Euler characteristic0
Schläfli type{6}
OrientableYes
Properties
Symmetry(G2×A1)/2, order 12
ConvexNo
Dimension vector(1,2)

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 ${\displaystyle \left\{{\dfrac {6}{1}}\right\}}$ 2
hexagonal-triangular coil ${\displaystyle \left\{{\dfrac {6}{1,2}}\right\}}$ 4
skew hexagon ${\displaystyle \left\{{\dfrac {6}{1,3}}\right\}}$ 3
skew triangle ${\displaystyle \left\{{\dfrac {6}{2,3}}\right\}}$ 3
skew hexagonal-triangular coil ${\displaystyle \left\{{\dfrac {6}{1,2,3}}\right\}}$ 5