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Loosely speaking, a figure tessellates if the plane can be covered by congruent copies of the figure. Trivially, a parallelogram tessellates (whereas, for example, a regular pentagon doesn't). Many modifications of a parallelogram also tessellate.

Here the figure that tessellates is the polygon AEBF'CE'DF, a modification of the parallelogram ABCD. (The unlabeled point E' is the translation of point E by vector DA; similarly for F'.)

For more, see GEOMETRY IN ACTION, Chapter 7.