Tessellations

Part 3: Constructing Tessellations

As mentioned in Part 1, only three types of regular tessellations exist; these use rectangles, triangles, or hexagons. Semi-regular tessellations combine two polygons that share a common side. Only a limited number of these 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 the "diaper patterns" created by contemporary artists.

This page contains a Flash movie that 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.

Demonstration requires the plug-in for Macromedia Flash version 6 or later.
File Size: 34 KB.
Click Button 1 or 2 to view.

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