Regular Division of the Plane

Regular division of the plane involves partitioning a flat surface into equal, non-overlapping regions, or polygons, arranged in a repeating, symmetrical pattern. These patterns are characterized by regular polygons (all sides and angles equal) meeting in a consistent way around each vertex. Such tilings can extend infinitely without gaps or overlaps, creating a harmonious and uniform design. Examples include tiling with equilateral triangles, squares, or regular hexagons. This concept is fundamental in fields like geometry, art, and crystallography, illustrating how complex, ordered patterns can fill a plane systematically and aesthetically.