Parallelogon

In geometry, a parallelogon is a polygon with parallel opposite sides (hence the name) that can tile a plane by translation (rotation is not permitted). Parallelogons have an even number of sides and opposite sides that are equal in length. A less obvious corollary is that parallelogons can only have either four or six sides; Parallelogons have 180-degree rotational symmetry around the center. A four-sided parallelogon is called a parallelogram. The faces of a parallelohedron (the three dimensional analogue) are called parallelogons. Quadrilateral and hexagonal parallelogons each have varied geometric symmetric forms. They all have central inversion symmetry, order 2. Every convex parallelogon is a zonogon, but hexagonal parallelogons enable the possibility of nonconvex polygons. A parallelogram can tile the plane as a distorted square tiling while a hexagonal parallelogon can tile the plane as a distorted regular hexagonal tiling.