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2. Pythagorean tiling - Wikipedia

   en.wikipedia.org/wiki/Pythagorean_tiling

   A Pythagorean tiling Street Musicians at the Door, Jacob Ochtervelt, 1665.As observed by Nelsen 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.

3. Tessellation - Wikipedia

   en.wikipedia.org/wiki/Tessellation

   A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular ...

4. Einstein problem - Wikipedia

   en.wikipedia.org/wiki/Einstein_problem

   Aperiodic tiling with "Tile(1,1)". The tiles are colored according to their rotational orientation modulo 60 degrees. [1] ( Smith, Myers, Kaplan, and Goodman-Strauss) In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles; that is, a shape that can tessellate space but only in a nonperiodic way.

5. Aperiodic tiling - Wikipedia

   en.wikipedia.org/wiki/Aperiodic_tiling

   An aperiodic tiling using a single shape and its reflection, discovered by David Smith. An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types (or prototiles) is aperiodic if copies of these tiles can form only non- periodic tilings.

6. Euclidean tilings by convex regular polygons - Wikipedia

   en.wikipedia.org/wiki/Euclidean_tilings_by...

   Euclidean tilings by convex regular polygons. A regular tiling has one type of regular face. A semiregular or uniform tiling has one type of vertex, but two or more types of faces. A k -uniform tiling has k types of vertices, and two or more types of regular faces. A non-edge-to-edge tiling can have different-sized regular faces.

7. Penrose tiling - Wikipedia

   en.wikipedia.org/wiki/Penrose_tiling

   Penrose tiling. A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does not contain arbitrarily large periodic regions or patches. However, despite their lack of translational symmetry, Penrose tilings may have both ...