Parallelogon


In geometry, a parallelogon is a polygon with parallel opposite sides that can tile a plane by translation.
Parallelogons have four or six sides, opposite sides that are equal in length, and 180-degree rotational symmetry around the center. A four-sided parallelogon is a parallelogram.
The three-dimensional analogue of a parallelogon is a parallelohedron. All faces of a parallelohedron are parallelogons.

Two polygonal types

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.

Geometric variations

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.