Skew triangle

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Skew triangle
Rank2
TypeRegular
Space3D Euclidean space
Notation
Schläfli symbol

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[edit | edit source]

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[edit | edit source]

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

Hexagons in Euclidean space
Name Extended Schläfli symbol Dimensions
hexagon 2
hexagonal-triangular coil 4
skew hexagon 3
skew triangle 3
skew hexagonal-triangular coil 5