Parallelogon


A parallelogon is a polygon such that images of the polygon will tile the plane when fitted together along entire sides, without rotation.
A parallelogon must have an even number of sides and opposite sides must be equal in length and parallel. A less obvious corollary is that all parallelogons have either four or six sides; a four-sided parallelogon is called a parallelogram. In general a parallelogon has 180-degree rotational symmetry around its center.
The faces of a parallelohedron are parallelogons.

Two polygonal types

Quadrilateral and hexagonal parallelogons each have varied geometric symmetric forms. In general 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.