"Offset polygons" is a limited technique for creating new tessellations.
The basic idea is to take a relatively simple polygon and deliberately
put copies of the polygon together so that vertices are not shared and that sides are not lined up.
Example of non-shared vertices and offset
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Here are some example tilings:
Offset squares
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Offset equilateral triangles
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Offset regular hexagons
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The variations of these examples are infinite. For example, you
can enlarge the offset in the first example as follows:
Squares with a different offset size (the squares are colored
red to contrast with the white spaces)
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| The important thing to remember is that joining sides exactly
edge-to-edge and vertex-to-vertex is not necessary when making
tessellations. |
  
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Real examples of offset polygons:
 
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 If you would like to experiment with offset polygons, go to the
templates page, print out some regular polygons, cut, and experiment.
Or, you can create your own simple polygon (such as a rectangle),
make copies, and experiment.
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