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A Penrose tiling with rhombi exhibiting fivefold symmetry. 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.
An example of such a tiling is shown in the adjacent diagram (see the image description for more information). A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic . [ 3 ]
However, an aperiodic set of tiles can only produce non-periodic tilings. [1] [2] Infinitely many distinct tilings may be obtained from a single aperiodic set of tiles. [3] The best-known examples of an aperiodic set of tiles are the various Penrose tiles. [4] [5] The known aperiodic sets of prototiles are seen on the list of aperiodic sets of ...
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]
English: A Penrose tiling (P3) using thick and thin rhombi. Note the aperiodic structure, shared by all Penrose tilings. Note the aperiodic structure, shared by all Penrose tilings. This particular Penrose tiling exhibits exact five-fold symmetry.
English: A Penrose tiling using Penrose's original set of six tiles (the "P1" set). If this is considered as a packing of pentagons only, the packing fraction is 0.809 [1] . Date
A Penrose tiling is a nonperiodic tiling generated by an aperiodic set of prototiles named after Roger Penrose, who investigated these sets in the 1970s.Among the infinitely many possible tilings there are two that possess both reflection symmetry and fivefold rotational symmetry, as in the diagram, and the term Penrose tiling usually refers to both.
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