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  2. Penrose tiling - Wikipedia

    en.wikipedia.org/wiki/Penrose_tiling

    The pattern represented by every finite patch of tiles in a Penrose tiling occurs infinitely many times throughout the tiling. They are quasicrystals: implemented as a physical structure a Penrose tiling will produce diffraction patterns with Bragg peaks and five-fold symmetry, revealing the repeated patterns and fixed orientations of its tiles ...

  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. Tilings and patterns - Wikipedia

    en.wikipedia.org/wiki/Tilings_and_patterns

    978-0-716-71193-3. OCLC. 13092426. Dewey Decimal. 511.6. LC Class. QA166.8.G78. Tilings and patterns is a book by mathematicians Branko Grünbaum and Geoffrey Colin Shephard published in 1987 by W.H. Freeman. The book was 10 years in development, and upon publication it was widely reviewed and highly acclaimed.

  5. Mosaic - Wikipedia

    en.wikipedia.org/wiki/Mosaic

    A mosaic is a pattern or image made of small regular or irregular pieces of colored stone, glass or ceramic, held in place by plaster / mortar, and covering a surface. [1] Mosaics are often used as floor and wall decoration, and were particularly popular in the Ancient Roman world. Mosaic today includes not just murals and pavements, but also ...

  6. 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.

  7. Cairo pentagonal tiling - Wikipedia

    en.wikipedia.org/wiki/Cairo_pentagonal_tiling

    Properties. face-transitive. In geometry, a Cairo pentagonal tiling is a tessellation of the Euclidean plane by congruent convex pentagons, formed by overlaying two tessellations of the plane by hexagons and named for its use as a paving design in Cairo. It is also called MacMahon's net[1] after Percy Alexander MacMahon, who depicted it in his ...

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