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- Ammann–Beenker_tiling abstract "In geometry, an Ammann–Beenker tiling is a nonperiodic tiling which can be generated either by an aperiodic set of prototiles as done by Robert Ammann in the 1970s, or by the cut-and-project method as done independently by F. P. M. Beenker.Because all tilings obtained with the tiles are non-periodic, Ammann–Beenker tilings are considered aperiodic tilings. They are one of the five sets of tilings discovered by Ammann and described in Tilings and Patterns.The Ammann–Beenker tilings have many properties similar to the more famous Penrose tilings, most notably:They are nonperiodic, which means that they lack any translational symmetry.Any finite region (patch) in a tiling appears infinitely many times in that tiling and, in fact, in any other tiling. Thus, the infinite tilings all look similar to one another, if one looks only at finite patches.They are quasicrystalline: implemented as a physical structure an Ammann–Beenker tiling will produce Bragg diffraction; the diffractogram reveals both the underlying eightfold symmetry and the long-range order. This order reflects the fact that the tilings are organized, not through translational symmetry, but rather through a process sometimes called \"deflation\" or \"inflation.\"Various methods to describe the tilings have been proposed: matching rules, substitutions, cut and project schemes and coverings. In 1987 Wang, Chen and Kuo announced the discovery of a quasicrystal with octagonal symmetry.".
- Ammann–Beenker_tiling thumbnail Ammann-Beenker_A5_in_blue_and_pink.svg?width=300.
- Ammann–Beenker_tiling wikiPageExternalLink ammann_beenker.
- Ammann–Beenker_tiling wikiPageExternalLink Ammann_Text.pdf.
- Ammann–Beenker_tiling wikiPageExternalLink oct01.htm.
- Ammann–Beenker_tiling wikiPageID "19292825".
- Ammann–Beenker_tiling wikiPageLength "10900".
- Ammann–Beenker_tiling wikiPageOutDegree "40".
- Ammann–Beenker_tiling wikiPageRevisionID "676940763".
- Ammann–Beenker_tiling wikiPageWikiLink Ammann_bar.
- Ammann–Beenker_tiling wikiPageWikiLink Ammann_bars.
- Ammann–Beenker_tiling wikiPageWikiLink Aperiodic_tiling.
- Ammann–Beenker_tiling wikiPageWikiLink Beenker.
- Ammann–Beenker_tiling wikiPageWikiLink Braggs_law.
- Ammann–Beenker_tiling wikiPageWikiLink Category:Aperiodic_tilings.
- Ammann–Beenker_tiling wikiPageWikiLink Category:Discrete_geometry.
- Ammann–Beenker_tiling wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Ammann–Beenker_tiling wikiPageWikiLink Geometry.
- Ammann–Beenker_tiling wikiPageWikiLink John_Horton_Conway.
- Ammann–Beenker_tiling wikiPageWikiLink Pell_number.
- Ammann–Beenker_tiling wikiPageWikiLink Penrose_tiling.
- Ammann–Beenker_tiling wikiPageWikiLink Prototile.
- Ammann–Beenker_tiling wikiPageWikiLink Quasicrystal.
- Ammann–Beenker_tiling wikiPageWikiLink Rhombus.
- Ammann–Beenker_tiling wikiPageWikiLink Robert_Ammann.
- Ammann–Beenker_tiling wikiPageWikiLink Silver_ratio.
- Ammann–Beenker_tiling wikiPageWikiLink Special_right_triangle.
- Ammann–Beenker_tiling wikiPageWikiLink Square.
- Ammann–Beenker_tiling wikiPageWikiLink Substitution_(logic).
- Ammann–Beenker_tiling wikiPageWikiLink Tessellation.
- Ammann–Beenker_tiling wikiPageWikiLink Tesseract.
- Ammann–Beenker_tiling wikiPageWikiLink Tesseractic_honeycomb.
- Ammann–Beenker_tiling wikiPageWikiLink Translational_symmetry.
- Ammann–Beenker_tiling wikiPageWikiLink File:8-8_duoprism_ortho-Dih8.png.
- Ammann–Beenker_tiling wikiPageWikiLink File:Ammann-Beenker_A5_in_blue_and_pink.svg.
- Ammann–Beenker_tiling wikiPageWikiLink File:Ammann-Beenker_tiling,_region_of_acceptance_domain_and_corresponding_vertex_figure,_type_A.png.
- Ammann–Beenker_tiling wikiPageWikiLink File:Ammann-Beenker_tiling,_region_of_acceptance_domain_and_corresponding_vertex_figure,_type_B.png.
- Ammann–Beenker_tiling wikiPageWikiLink File:Ammann-Beenker_tiling,_region_of_acceptance_domain_and_corresponding_vertex_figure,_type_C.png.
- Ammann–Beenker_tiling wikiPageWikiLink File:Ammann-Beenker_tiling,_region_of_acceptance_domain_and_corresponding_vertex_figure,_type_D.png.
- Ammann–Beenker_tiling wikiPageWikiLink File:Ammann-Beenker_tiling,_region_of_acceptance_domain_and_corresponding_vertex_figure,_type_E.png.
- Ammann–Beenker_tiling wikiPageWikiLink File:Ammann-Beenker_tiling,_region_of_acceptance_domain_and_corresponding_vertex_figure,_type_F.png.
- Ammann–Beenker_tiling wikiPageWikiLink File:Ammann-Beenker_tiling_example.png.
- Ammann–Beenker_tiling wikiPageWikiLink File:Ammannbeenker.PNG.
- Ammann–Beenker_tiling wikiPageWikiLink File:Ammannbeenkerbars.png.
- Ammann–Beenker_tiling wikiPageWikiLink File:Ammannbeenkerbars2.png.
- Ammann–Beenker_tiling wikiPageWikiLink File:Ammannbeenkerreplace.PNG.
- Ammann–Beenker_tiling wikiPageWikiLink File:Ammannbeenkerreplace2.svg.
- Ammann–Beenker_tiling wikiPageWikiLinkText "Ammann A4 tiles".
- Ammann–Beenker_tiling wikiPageWikiLinkText "Ammann A5 tiles".
- Ammann–Beenker_tiling wikiPageWikiLinkText "Ammann–Beenker tiling".
- Ammann–Beenker_tiling wikiPageUsesTemplate Template:Tessellation.
- Ammann–Beenker_tiling subject Category:Aperiodic_tilings.
- Ammann–Beenker_tiling subject Category:Discrete_geometry.
- Ammann–Beenker_tiling type Pattern.
- Ammann–Beenker_tiling type Polytope.
- Ammann–Beenker_tiling type Redirect.
- Ammann–Beenker_tiling comment "In geometry, an Ammann–Beenker tiling is a nonperiodic tiling which can be generated either by an aperiodic set of prototiles as done by Robert Ammann in the 1970s, or by the cut-and-project method as done independently by F. P. M. Beenker.Because all tilings obtained with the tiles are non-periodic, Ammann–Beenker tilings are considered aperiodic tilings.".
- Ammann–Beenker_tiling label "Ammann–Beenker tiling".
- Ammann–Beenker_tiling sameAs Q4747168.
- Ammann–Beenker_tiling sameAs m.04lhb1w.
- Ammann–Beenker_tiling sameAs Q4747168.
- Ammann–Beenker_tiling wasDerivedFrom Ammann–Beenker_tiling?oldid=676940763.
- Ammann–Beenker_tiling depiction Ammann-Beenker_A5_in_blue_and_pink.svg.
- Ammann–Beenker_tiling isPrimaryTopicOf Ammann–Beenker_tiling.