Parallelogon

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A parallelogon is a polygon with an even number of sides, such that pairwise opposite sides are parallel. A quadrilateral parallelogon is a parallelogram. Each side of a parallelogon is parallel to the opposite side.

If the opposite sides of a six-sided parallelogon are equal in length, then that hexagon can tile the plane. Every quadrilateral tiles the plane, because every quadrilateral is half of a six-sided parallelogon with opposite sides equal in length. Just as the lengths of the sides of a parallelogram follow an a, b, a, b pattern, so the lengths of the sides of the above-mentioned polygon follow an a, b, c, a, b, c pattern.

If 2n is the number of sides, then consecutive sides can be numbered 1, 2, 3...n, n + 1, n + 2,....2n. The opposite side is the side whose number is congruent modulo n. For example, side 3 and side n + 3 are opposite.