# Skew triangle

Skew triangle
Rank2
TypeRegular
Space3D Euclidean space
Notation
Schläfli symbol${\displaystyle \{3\}\#\{\}}$
${\displaystyle \{3\}\#\{2\}}$
${\displaystyle \left\{{\dfrac {6}{2,3}}\right\}}$
Elements
Edges6
Vertices6
Related polytopes
ArmyTrip
Convex hullTriangular prism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryA2×A1, order 12
ConvexNo
Dimension vector(1,2)

The skew triangle is a regular skew polygon in 3D Euclidean space. Despite its name it has 6 sides and 6 vertices. It is the result of blending a triangle with a digon. Since the triangle is not 2-colorable the result has twice as many vertices and edges as the triangle.

Its edges form the diagonals of the rectangular faces of a general triangular prism.

## Related polytopes

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

### Other skew hexagons

The skew triangle 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