Tilingssystemer

Tilingssystemer, often translated as tiling systems or tessellations, refer to the arrangement of geometric shapes called tiles to cover a surface without any gaps or overlaps. These arrangements can be found in nature, art, architecture, and mathematics. The fundamental principle of a tiling system is that the sum of the angles of the tiles meeting at any vertex must equal 360 degrees.

There are several types of tilings. Regular tilings use only one type of regular polygon, such as equilateral triangles, squares, or regular hexagons. Only these three regular polygons can tile the plane on their own. Semiregular tilings, also known as Archimedean tilings, use two or more types of regular polygons, arranged in a way that all vertices are identical. There are 8 such semiregular tilings.

Beyond regular and semiregular tilings, there are irregular tilings that can use a variety of shapes, including polygons with more sides or even curved shapes, as long as they can fit together without gaps or overlaps. Islamic art is famous for its intricate and complex tiling patterns, often featuring stars and polygons. In mathematics, tilings are studied in fields like geometry, combinatorics, and topology, with concepts like aperiodic tilings (like Penrose tilings) exploring patterns that do not repeat. The study of tilings has practical applications in areas such as crystallography, computer graphics, and materials science.