A tesselation is a tiling of the plane so that there are no gaps or overlaps - like a tiled countertop. M.C. Escher used tessellations in much of his work. Some were pure tessellations, like the first picture below, others used a tiling that changed into something else, like the second and third pictures below. The following images are his works (for more see the official M.C. Escher site).
Shodor has a great interactive website where you can make your own tessellations with the help of a Java Applet. I used it to make the tessellation at the top of this post. You can change colors and can choose to begin with a triangle, rectangle or hexagon and can alter these shapes using their sides or corners. I started with a hexagon. The computer helps you alter them in ways that will fit together. Have fun!
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