Parallelogon

A parallelogon is a polygon such that images of the polygon under translations only tile the plane when fitted together along entire sides.

A parallelogon must have an even number of sides and opposite sides must be equal in length and parallel (hence the name). A less obvious restriction is that a parallelogon can only have four or six sides; a four-sided parallelogon is a parallelogram. In general a parallelogon has 180-degree rotational symmetry around its center.

Quadrilateral and hexagonal parallelogons each have varied geometric symmetric forms. In general they all have central inversion symmetry, order 2. Hexagonal parallelogons enable the possibility of nonconvex polygons.

Parallelogram can tile the plane as a distorted square tiling while hexagonal parallelogon can tiling the plane as a distorted regular hexagonal tiling.

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