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A tessellation is a subdivision of a space into nonoverlapping regions that fill the space completely. In GIS, a variety of tessellations perform multiple roles in both spatial data representation and spatial data analysis. This entry identifies some of the most important tessellations, describes their fundamental characteristics, and outlines their major applications. When the space is two-dimensional, the tessellation is called planar. Since this is the most frequently encountered situation in GIS, it is emphasized here.

A major distinction is made between regular tessellations, in which all the regions are identical regular polygons, and irregular tessellations, when they are not. There are three regular, planar tessellations: those consisting of triangles, squares, and hexagons. Regular tessellations possess two characteristics that favor their use as both spatial ...

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