To tessellate a surface is to cover it with shapes without leaving any gaps. In mosaics, surfaces are often tesselated with irregular shapes fitted closely together. In mathematics, a shape is said to tessellate if copies of it can be arranged repeatedly on a flat surface without leaving any spaces. For example, squares tessellate (as on a chessboard), and so do hexagons (think of a honeycomb pattern). Octogons do not tesslate, but a surface can be tessellated with a combination of octagons and squares. Many striking geometric pavements can be created from different tessellations of geometric and interlocking shapes.
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