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  2. List of aperiodic sets of tiles - Wikipedia

    en.wikipedia.org/wiki/List_of_aperiodic_sets_of...

    In geometry, a tiling is a partition of the plane (or any other geometric setting) into closed sets (called tiles), without gaps or overlaps (other than the boundaries of the tiles). [1] A tiling is considered periodic if there exist translations in two independent directions which map the tiling onto itself.

  3. Einstein problem - Wikipedia

    en.wikipedia.org/wiki/Einstein_problem

    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.

  4. Aperiodic tiling - Wikipedia

    en.wikipedia.org/wiki/Aperiodic_tiling

    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. The Penrose tilings are a well-known example of aperiodic tilings. [1] [2]

  5. Ammann–Beenker tiling - Wikipedia

    en.wikipedia.org/wiki/Ammann–Beenker_tiling

    The Ammann–Beenker tilings are closely related to the silver ratio (+) and the Pell numbers.. the substitution scheme ; introduces the ratio as a scaling factor: its matrix is the Pell substitution matrix, and the series of words produced by the substitution have the property that the number of s and s are equal to successive Pell numbers.

  6. Penrose tiling - Wikipedia

    en.wikipedia.org/wiki/Penrose_tiling

    Concretely, if A S has side lengths (1, 1, φ), then A L has side lengths (φ, φ, 1). B-tiles can be related to such A-tiles in two ways: If B S has the same size as A L then B L is an enlarged version φ A S of A S, with side lengths (φ, φ, φ 2 = 1 + φ) – this decomposes into an A L tile and A S tile joined along a common side of length 1.

  7. Quasicrystal - Wikipedia

    en.wikipedia.org/wiki/Quasicrystal

    The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled, e.g., the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two directions.

  8. Template:Article templates/Anatomy - Wikipedia

    en.wikipedia.org/wiki/Template:Article_templates/...

    Template documentation This template may have no transclusions , because it is substituted by a tool or script, it is used as part of a short-term or less active Wikipedia process, or for some other reason.

  9. Nonmetallic material - Wikipedia

    en.wikipedia.org/wiki/Nonmetallic_material

    Nonmetallic material, or in nontechnical terms a nonmetal, refers to materials which are not metals. Depending upon context it is used in slightly different ways. In everyday life it would be a generic term for those materials such as plastics, wood or ceramics which are not typical metals such as the iron alloys used in bridges.