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Fine art: Use of group theory, self-replicating shapes in art [21] [22] Escher, M. C. 1898–1972: Fine art: Exploration of tessellations, hyperbolic geometry, assisted by the geometer H. S. M. Coxeter [19] [23] Farmanfarmaian, Monir: 1922–2019: Fine art: Geometric constructions exploring the infinite, especially mirror mosaics [24] Ferguson ...
Escher used irregular polygons when tiling the plane and often used reflections, glide reflections, and translations to obtain further patterns. Many of his works contain impossible constructions, made using geometrical objects which set up a contradiction between perspective projection and three dimensions, but are pleasant to the human sight.
Star polygons and polygonal compounds are the basis for numerous figures of significance in arts and culture. The figure may be the border or interior of the polygon, or one or more closed polygonal paths that include all of the border and also have some legs crossing the interior.
Star polygons feature prominently in art and culture. Such polygons may or may not be regular, but they are always highly symmetrical. Examples include: The {5/2} star pentagon is also known as a pentalpha or pentangle, and historically has been considered by many magical and religious cults to have occult significance.
Escher worked primarily in the media of lithographs and woodcuts, although the few mezzotints he made are considered to be masterpieces of the technique. In his graphic art, he portrayed mathematical relationships among shapes, figures, and space. Integrated into his prints were mirror images of cones, spheres, cubes, rings, and spirals. [45]
A recurring motif is the 8-pointed star, often seen in Islamic tilework; it is made of two squares, one rotated 45 degrees with respect to the other. The fourth basic shape is the polygon, including pentagons and octagons.
A regular tessellation is a highly symmetric, edge-to-edge tiling made up of regular polygons, all of the same shape. There are only three regular tessellations: those made up of equilateral triangles, squares, or regular hexagons. All three of these tilings are isogonal and monohedral. [26] A Pythagorean tiling is not an edge‑to‑edge tiling.
Polygon mesh representing a dolphin, considered to be a low poly model by modern standards Low Poly Art, depicting a Kingfisher. Low poly is a polygon mesh in 3D computer graphics that has a relatively small number of polygons.