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- Penrose_tiling abstract "A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated these sets in the 1970s. The aperiodicity of the Penrose prototiles implies that a shifted copy of a Penrose tiling will never match the original. A Penrose tiling may be constructed so as to exhibit both reflection symmetry and fivefold rotational symmetry, as in the diagram at the right. A Penrose tiling has many remarkable properties, most notably:It is non-periodic, which means that it lacks any translational symmetry. It is self-similar, so the same patterns occur at larger and larger scales. Thus, the tiling can be obtained through "inflation" (or "deflation") and any finite patch from the tiling occurs infinitely many times.It is a quasicrystal: implemented as a physical structure a Penrose tiling will produce Bragg diffraction and its diffractogram reveals both the fivefold symmetry and the underlying long range order.Various methods to construct Penrose tilings have been discovered, including matching rules, substitutions or subdivision rules, cut and project schemes and coverings.".
- Penrose_tiling thumbnail Penrose_Tiling_(Rhombi).svg?width=300.
- Penrose_tiling wikiPageExternalLink penrose_rhomb.
- Penrose_tiling wikiPageExternalLink penrose.html.
- Penrose_tiling wikiPageExternalLink ribbons.html.
- Penrose_tiling wikiPageExternalLink penrose.htm.
- Penrose_tiling wikiPageExternalLink pen01.htm.
- Penrose_tiling wikiPageExternalLink BKMM7xpc.htm.
- Penrose_tiling wikiPageID "26611936".
- Penrose_tiling wikiPageLength "42713".
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- Penrose_tiling wikiPageRevisionID "682098801".
- Penrose_tiling wikiPageWikiLink Albrecht_Dürer.
- Penrose_tiling wikiPageWikiLink Andrew_Wiles.
- Penrose_tiling wikiPageWikiLink Aperiodic_set_of_prototiles.
- Penrose_tiling wikiPageWikiLink Aperiodic_tiling.
- Penrose_tiling wikiPageWikiLink Bragg_diffraction.
- Penrose_tiling wikiPageWikiLink Braggs_law.
- Penrose_tiling wikiPageWikiLink Category:Aperiodic_tilings.
- Penrose_tiling wikiPageWikiLink Category:Discrete_geometry.
- Penrose_tiling wikiPageWikiLink Category:Mathematics_and_art.
- Penrose_tiling wikiPageWikiLink Chord_(geometry).
- Penrose_tiling wikiPageWikiLink CirKis.
- Penrose_tiling wikiPageWikiLink Concave_polygon.
- Penrose_tiling wikiPageWikiLink Congruence_(geometry).
- Penrose_tiling wikiPageWikiLink Crystal_structure.
- Penrose_tiling wikiPageWikiLink Decagon.
- Penrose_tiling wikiPageWikiLink Decision_problem.
- Penrose_tiling wikiPageWikiLink Dihedral_group.
- Penrose_tiling wikiPageWikiLink Dihedral_symmetry.
- Penrose_tiling wikiPageWikiLink Dodecahedron.
- Penrose_tiling wikiPageWikiLink Domino_Problem.
- Penrose_tiling wikiPageWikiLink Donald_Knuth.
- Penrose_tiling wikiPageWikiLink Drop_City.
- Penrose_tiling wikiPageWikiLink Euclidean_tilings_of_convex_regular_polygons.
- Penrose_tiling wikiPageWikiLink Eureka_(University_of_Cambridge_magazine).
- Penrose_tiling wikiPageWikiLink Fibonacci_number.
- Penrose_tiling wikiPageWikiLink File:Penrose_Tiling_(Rhombi).svg.
- Penrose_tiling wikiPageWikiLink File:Pentagon_with_half_dodecahedral_net.svg.
- Penrose_tiling wikiPageWikiLink File:Rhomb_pentagon.svg.
- Penrose_tiling wikiPageWikiLink Finite_set.
- Penrose_tiling wikiPageWikiLink Finite_subdivision_rule.
- Penrose_tiling wikiPageWikiLink Fractal.
- Penrose_tiling wikiPageWikiLink Girih_tiles.
- Penrose_tiling wikiPageWikiLink Golden_ratio.
- Penrose_tiling wikiPageWikiLink Golden_triangle_(mathematics).
- Penrose_tiling wikiPageWikiLink Group_(mathematics).
- Penrose_tiling wikiPageWikiLink Hao_Wang_(academic).
- Penrose_tiling wikiPageWikiLink Harmonices_Mundi.
- Penrose_tiling wikiPageWikiLink Isosceles.
- Penrose_tiling wikiPageWikiLink Isosceles_triangle.
- Penrose_tiling wikiPageWikiLink Jigsaw_puzzle.
- Penrose_tiling wikiPageWikiLink Johannes_Kepler.
- Penrose_tiling wikiPageWikiLink John_H._Conway.
- Penrose_tiling wikiPageWikiLink John_Horton_Conway.
- Penrose_tiling wikiPageWikiLink List_of_aperiodic_sets_of_tiles.
- Penrose_tiling wikiPageWikiLink Martin_Gardner.
- Penrose_tiling wikiPageWikiLink Martin_Kemp_(art_historian).
- Penrose_tiling wikiPageWikiLink Matrix_(mathematics).
- Penrose_tiling wikiPageWikiLink Net_(polyhedron).
- Penrose_tiling wikiPageWikiLink Nicolaas_Govert_de_Bruijn.
- Penrose_tiling wikiPageWikiLink Patterns_in_nature.
- Penrose_tiling wikiPageWikiLink Paul_Steinhardt.
- Penrose_tiling wikiPageWikiLink Pentagon.
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- Penrose_tiling wikiPageWikiLink Pentagram.
- Penrose_tiling wikiPageWikiLink Periodic_tiling.
- Penrose_tiling wikiPageWikiLink Peter_Lu.
- Penrose_tiling wikiPageWikiLink Pinwheel_tiling.
- Penrose_tiling wikiPageWikiLink Plane_(geometry).
- Penrose_tiling wikiPageWikiLink Prototile.
- Penrose_tiling wikiPageWikiLink Quaquaversal_tiling.
- Penrose_tiling wikiPageWikiLink Quasicrystal.
- Penrose_tiling wikiPageWikiLink Quasicrystals.
- Penrose_tiling wikiPageWikiLink Raphael_M._Robinson.
- Penrose_tiling wikiPageWikiLink Raphael_Robinson.
- Penrose_tiling wikiPageWikiLink Recursive_set.
- Penrose_tiling wikiPageWikiLink Reflection_symmetry.
- Penrose_tiling wikiPageWikiLink Regular_pentagon.
- Penrose_tiling wikiPageWikiLink Rhombus.
- Penrose_tiling wikiPageWikiLink Robert_Ammann.
- Penrose_tiling wikiPageWikiLink Robert_Berger_(mathematician).
- Penrose_tiling wikiPageWikiLink Roger_Penrose.
- Penrose_tiling wikiPageWikiLink Rotational_symmetry.
- Penrose_tiling wikiPageWikiLink San_Francisco_Transbay_development.
- Penrose_tiling wikiPageWikiLink Science_(journal).
- Penrose_tiling wikiPageWikiLink Scientific_American.
- Penrose_tiling wikiPageWikiLink Self-similarity.
- Penrose_tiling wikiPageWikiLink Set_(mathematics).
- Penrose_tiling wikiPageWikiLink Star_polygon.
- Penrose_tiling wikiPageWikiLink Subdivision_rule.
- Penrose_tiling wikiPageWikiLink Substitution_tiling.
- Penrose_tiling wikiPageWikiLink Tessellation.
- Penrose_tiling wikiPageWikiLink The_Mathematical_Intelligencer.
- Penrose_tiling wikiPageWikiLink Translation_(geometry).
- Penrose_tiling wikiPageWikiLink Translation_(mathematics).
- Penrose_tiling wikiPageWikiLink Translational_symmetry.
- Penrose_tiling wikiPageWikiLink Triangle.
- Penrose_tiling wikiPageWikiLink Uncountable_set.
- Penrose_tiling wikiPageWikiLink Uncountably_infinite.