Teselación

Teselación refers to the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps or gaps. These shapes are arranged in a repeating pattern that covers the entire surface. The most common examples are found in everyday life, such as floor tiles, bathroom tiles, and wallpaper patterns.

Geometric shapes that can be used for teselation include regular polygons like squares, triangles, and hexagons. It is also possible to create teselations with irregular polygons, provided they meet certain conditions. For instance, any quadrilateral can be used to teselate a plane. More complex shapes, including stars and even freeform designs, can also be used to create intricate and visually appealing patterns, often referred to as decorative or artistic teselations.

The study of teselations has roots in ancient civilizations, with examples found in Roman mosaics and Islamic art. Mathematically, teselations are explored within the field of geometry and crystallography. A particularly famous type is the semi-regular teselation, which uses two or more different regular polygons to tile a plane. The concept of symmetry plays a crucial role in understanding and classifying different types of teselations.