EXAMPLE 2 Tiling Starting from a Parallelogram

How can you make an Escher-like tiling by starting from a parallelogram?

Applying the first alternative of the criterion, start from a parallelogram, make a change to the boundary on one side, and then copy that change to the opposite side. Similarly, change one of the other two sides and copy that change on the side opposite it (see Figure 20.13). Revise as necessary, always making the same change to opposite sides. You might find it useful (as Escher did) to make your designs on graph paper, or you can work by cutting and taping together pieces of heavy paper.

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