As mentioned in above, only three types of regular tessellations exist; these use rectangles, triangles, or hexagons. Semi-regular tessellations combine two polygons that share a common edige; only a limited number of these shapes exist. To create more exotic tessellations, you can construct an irregular shape — or series of shapes — using a careful but simple methodology of polygon modification. This technique was used by M.C. Escher to create his famous “Metamorphosis” and is common in “diaper patterns.”
The video below dynamically illustrates two methods of tessellation construction. The first method shows how a single irregular tile can produce many different patterns. The second method shows how to create a metamorphosis with two different shapes that do not share a common edge through the use of transitional shapes. The demonstration requires the plug-in for Adobe Flash version 6 or later.