tesselláció

Tesselláció, also known as tiling, is the arrangement of geometric shapes, called tiles, to completely cover a plane without any overlaps or gaps. These tiles can be simple polygons like squares, triangles, or hexagons, or they can be more complex shapes. The edges of the tiles must meet exactly.

A tessellation is considered regular if it is made up of only one type of regular polygon. Only equilateral triangles, squares, and regular hexagons can form regular tessellations. Semi-regular tessellations, also known as uniform tessellations, are made up of two or more different regular polygons, where the arrangement of polygons around each vertex is identical.

Tessellations are found in various aspects of nature and art. For example, honeycomb structures are a natural example of hexagonal tessellation, providing efficient use of space and material. In art, tessellations have been used for centuries in mosaics, Islamic art, and the works of artists like M.C. Escher, who famously explored the mathematical and visual possibilities of repeating patterns and motifs that fit together perfectly. The study of tessellations is a branch of geometry and has applications in fields such as crystallography and computer graphics.