We have discussed regular and semiregular tilings in this section. In general, however,...

We have discussed regular and semiregular tilings in this section. In general, however, tilings can be divided into two kinds: periodic and nonperiodic. If a region of the tiling can be outlined, by constructing a grid or a lattice made up of equally spaced parallel lines, and a portion of that outlined region (the basic repeated tile) can be used to tile the plane, as shown in the following tiling, then the tiling is called periodic.

M. C. Escher created some of the most famous periodic tilings. Show that the following Escher tiling is periodic.

M. C. Escher “Symmetry Drawing E124” © 2005 The M. C. Escher Company-Holland. All rights reserved.

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