Tessellation
A tessellation is a pattern of flat shapes that fit together without any overlaps or gaps. All the tiles you can buy at Home Depot tessellate. Who would want a patio with holes?
Here are some familiar tessellations:
hexagons
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squares
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triangles
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Tessellations don't have to be just one shape. Here are a couple of 2-shape tesselations:
hexagons and triangles
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octagons and squares
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Tessellations don't even have to be regular geometric shapes! M.C. Escher made wild tesselations with pictures, like these birds (some going left, some right!)
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