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- Crystallographic_restriction_theorem abstract "The crystallographic restriction theorem in its basic form was based on the observation that the rotational symmetries of a crystal are usually limited to 2-fold, 3-fold, 4-fold, and 6-fold. However, quasicrystals can occur with other diffraction pattern symmetries, such as 5-fold; these were not discovered until 1982 by Dan Shechtman.Crystals are modeled as discrete lattices, generated by a list of independent finite translations (Coxeter 1989). Because discreteness requires that the spacings between lattice points have a lower bound, the group of rotational symmetries of the lattice at any point must be a finite group. The strength of the theorem is that not all finite groups are compatible with a discrete lattice; in any dimension, we will have only a finite number of compatible groups.".
- Crystallographic_restriction_theorem thumbnail Crystallographic_restriction_polygons.png?width=300.
- Crystallographic_restriction_theorem wikiPageExternalLink digbib.cgi?PPN378850199_0001.
- Crystallographic_restriction_theorem wikiPageExternalLink A2.html.
- Crystallographic_restriction_theorem wikiPageExternalLink 42.pdf.
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- Crystallographic_restriction_theorem wikiPageLength "16452".
- Crystallographic_restriction_theorem wikiPageOutDegree "59".
- Crystallographic_restriction_theorem wikiPageRevisionID "707158105".
- Crystallographic_restriction_theorem wikiPageWikiLink 5-cell_honeycomb.
- Crystallographic_restriction_theorem wikiPageWikiLink Algebraic_number.
- Crystallographic_restriction_theorem wikiPageWikiLink American_Mathematical_Monthly.
- Crystallographic_restriction_theorem wikiPageWikiLink Ammann–Beenker_tiling.
- Crystallographic_restriction_theorem wikiPageWikiLink Aperiodic_tiling.
- Crystallographic_restriction_theorem wikiPageWikiLink Category:Articles_containing_proofs.
- Crystallographic_restriction_theorem wikiPageWikiLink Category:Crystallography.
- Crystallographic_restriction_theorem wikiPageWikiLink Category:Group_theory.
- Crystallographic_restriction_theorem wikiPageWikiLink Category:Theorems_in_algebra.
- Crystallographic_restriction_theorem wikiPageWikiLink Cross-polytope.
- Crystallographic_restriction_theorem wikiPageWikiLink Crystal.
- Crystallographic_restriction_theorem wikiPageWikiLink Crystallographic_point_group.
- Crystallographic_restriction_theorem wikiPageWikiLink Crystallography.
- Crystallographic_restriction_theorem wikiPageWikiLink Dan_Shechtman.
- Crystallographic_restriction_theorem wikiPageWikiLink Determinant.
- Crystallographic_restriction_theorem wikiPageWikiLink Elemente_der_Mathematik.
- Crystallographic_restriction_theorem wikiPageWikiLink Euclidean_space.
- Crystallographic_restriction_theorem wikiPageWikiLink Euclidean_vector.
- Crystallographic_restriction_theorem wikiPageWikiLink Eulers_totient_function.
- Crystallographic_restriction_theorem wikiPageWikiLink F4_(mathematics).
- Crystallographic_restriction_theorem wikiPageWikiLink Finite_group.
- Crystallographic_restriction_theorem wikiPageWikiLink Fundamental_theorem_of_arithmetic.
- Crystallographic_restriction_theorem wikiPageWikiLink Group_(mathematics).
- Crystallographic_restriction_theorem wikiPageWikiLink Group_action.
- Crystallographic_restriction_theorem wikiPageWikiLink Hypercube.
- Crystallographic_restriction_theorem wikiPageWikiLink Hypercubic_honeycomb.
- Crystallographic_restriction_theorem wikiPageWikiLink Improper_rotation.
- Crystallographic_restriction_theorem wikiPageWikiLink Integer.
- Crystallographic_restriction_theorem wikiPageWikiLink Isolated_point.
- Crystallographic_restriction_theorem wikiPageWikiLink Isometry.
- Crystallographic_restriction_theorem wikiPageWikiLink Isometry_group.
- Crystallographic_restriction_theorem wikiPageWikiLink Lattice_(group).
- Crystallographic_restriction_theorem wikiPageWikiLink Linear_independence.
- Crystallographic_restriction_theorem wikiPageWikiLink Matrix_(mathematics).
- Crystallographic_restriction_theorem wikiPageWikiLink Order_(group_theory).
- Crystallographic_restriction_theorem wikiPageWikiLink Orthonormal_basis.
- Crystallographic_restriction_theorem wikiPageWikiLink Penrose_tiling.
- Crystallographic_restriction_theorem wikiPageWikiLink Physical_Review_Letters.
- Crystallographic_restriction_theorem wikiPageWikiLink Point_groups_in_three_dimensions.
- Crystallographic_restriction_theorem wikiPageWikiLink Prime_number.
- Crystallographic_restriction_theorem wikiPageWikiLink Quasicrystal.
- Crystallographic_restriction_theorem wikiPageWikiLink Regular_polygon.
- Crystallographic_restriction_theorem wikiPageWikiLink Rotation_matrix.
- Crystallographic_restriction_theorem wikiPageWikiLink Rotational_symmetry.
- Crystallographic_restriction_theorem wikiPageWikiLink Similarity_invariance.
- Crystallographic_restriction_theorem wikiPageWikiLink Space_group.
- Crystallographic_restriction_theorem wikiPageWikiLink Tessellation.
- Crystallographic_restriction_theorem wikiPageWikiLink Trace_(linear_algebra).
- Crystallographic_restriction_theorem wikiPageWikiLink Translation.
- Crystallographic_restriction_theorem wikiPageWikiLink Wallpaper_group.
- Crystallographic_restriction_theorem wikiPageWikiLink Wikt:oblique.
- Crystallographic_restriction_theorem wikiPageWikiLink File:Crystallographic_restriction.png.
- Crystallographic_restriction_theorem wikiPageWikiLink File:Crystallographic_restriction_2.png.
- Crystallographic_restriction_theorem wikiPageWikiLink File:Crystallographic_restriction_polygons.png.
- Crystallographic_restriction_theorem wikiPageWikiLinkText "Crystallographic restriction theorem".
- Crystallographic_restriction_theorem wikiPageWikiLinkText "compatible".
- Crystallographic_restriction_theorem wikiPageWikiLinkText "crystallographic restriction theorem".
- Crystallographic_restriction_theorem wikiPageWikiLinkText "crystallographic restriction".
- Crystallographic_restriction_theorem wikiPageWikiLinkText "crystallographic".
- Crystallographic_restriction_theorem wikiPageWikiLinkText "restricted".
- Crystallographic_restriction_theorem wikiPageUsesTemplate Template:Citation.
- Crystallographic_restriction_theorem wikiPageUsesTemplate Template:Harv.
- Crystallographic_restriction_theorem wikiPageUsesTemplate Template:Use_dmy_dates.
- Crystallographic_restriction_theorem subject Category:Articles_containing_proofs.
- Crystallographic_restriction_theorem subject Category:Crystallography.
- Crystallographic_restriction_theorem subject Category:Group_theory.
- Crystallographic_restriction_theorem subject Category:Theorems_in_algebra.
- Crystallographic_restriction_theorem type Biophysic.
- Crystallographic_restriction_theorem type Physic.
- Crystallographic_restriction_theorem type Proof.
- Crystallographic_restriction_theorem type Theorem.
- Crystallographic_restriction_theorem comment "The crystallographic restriction theorem in its basic form was based on the observation that the rotational symmetries of a crystal are usually limited to 2-fold, 3-fold, 4-fold, and 6-fold. However, quasicrystals can occur with other diffraction pattern symmetries, such as 5-fold; these were not discovered until 1982 by Dan Shechtman.Crystals are modeled as discrete lattices, generated by a list of independent finite translations (Coxeter 1989).".
- Crystallographic_restriction_theorem label "Crystallographic restriction theorem".
- Crystallographic_restriction_theorem sameAs Q3527223.
- Crystallographic_restriction_theorem sameAs Teorema_de_restricción_cristalográfica.
- Crystallographic_restriction_theorem sameAs Théorème_de_restriction_cristallographique.
- Crystallographic_restriction_theorem sameAs m.06ws0p.
- Crystallographic_restriction_theorem sameAs Q3527223.
- Crystallographic_restriction_theorem wasDerivedFrom Crystallographic_restriction_theorem?oldid=707158105.
- Crystallographic_restriction_theorem depiction Crystallographic_restriction_polygons.png.
- Crystallographic_restriction_theorem isPrimaryTopicOf Crystallographic_restriction_theorem.