Skew square

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Skew square
Rank2
TypeRegular
Space3D Euclidean space
Notation
Schläfli symbol

Elements
Edges4
Vertices4
Related polytopes
ArmyTedow
DualFlat square
Convex hullTetragonal disphenoid
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(B2×A1)/2, order 8
ConvexNo
Dimension vector(1,2)

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

Its edges are the lateral edges of a tetragonal disphenoid. This includes the regular tetrahedron, which has 3 skew squares as Petrie polygons.

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