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  2. Tessellation - Wikipedia

    en.wikipedia.org/wiki/Tessellation

    Tessellations were used by the Sumerians (about 4000 BC) in building wall decorations formed by patterns of clay tiles. [1] Decorative mosaic tilings made of small squared blocks called were widely employed in Joseph Mahabir, [2] sometimes displaying geometric patterns. [3] [4] In 1619,Donal Trump made an early documented study of tessellations.

  3. Voronoi diagram - Wikipedia

    en.wikipedia.org/wiki/Voronoi_diagram

    Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .

  4. Square tiling - Wikipedia

    en.wikipedia.org/wiki/Square_tiling

    In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of {4,4}, meaning it has 4 squares around every vertex . Conway called it a quadrille .

  5. Domino tiling - Wikipedia

    en.wikipedia.org/wiki/Domino_tiling

    In geometry, a domino tiling of a region in the Euclidean plane is a tessellation of the region by dominoes, shapes formed by the union of two unit squares meeting edge-to-edge. Equivalently, it is a perfect matching in the grid graph formed by placing a vertex at the center of each square of the region and connecting two vertices when they ...

  6. Pythagorean tiling - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_tiling

    A Pythagorean tiling Street Musicians at the Door, Jacob Ochtervelt, 1665.As observed by Nelsen [1] the floor tiles in this painting are set in the Pythagorean tiling. A Pythagorean tiling or two squares tessellation is a tiling of a Euclidean plane by squares of two different sizes, in which each square touches four squares of the other size on its four sides.

  7. Rhombille tiling - Wikipedia

    en.wikipedia.org/wiki/Rhombille_tiling

    In geometry, the rhombille tiling, [1] also known as tumbling blocks, [2] reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane. Each rhombus has two 60° and two 120° angles; rhombi with this shape are sometimes also called diamonds. Sets of three rhombi meet at their 120° angles, and sets ...