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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 symmetries, such as 5-fold; these were not discovered until 1982, when a diffraction pattern out of a quasicrystal was first seen by the Israeli scientist Dan Shechtman, who won the 2011 Nobel Prize in Chemistry for his discovery.Prior to the discovery of quasicrystals, crystals were 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.
- Crystallographic_restriction_theorem wikiPageID "2218040".
- Crystallographic_restriction_theorem wikiPageRevisionID "604423001".
- Crystallographic_restriction_theorem hasPhotoCollection Crystallographic_restriction_theorem.
- 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 Abstraction100002137.
- Crystallographic_restriction_theorem type Communication100033020.
- Crystallographic_restriction_theorem type Message106598915.
- Crystallographic_restriction_theorem type Proposition106750804.
- Crystallographic_restriction_theorem type Statement106722453.
- Crystallographic_restriction_theorem type Theorem106752293.
- Crystallographic_restriction_theorem type TheoremsInAlgebra.
- 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.".
- Crystallographic_restriction_theorem label "Crystallographic restriction theorem".
- Crystallographic_restriction_theorem label "Teorema de restricción cristalográfica".
- Crystallographic_restriction_theorem label "Théorème de restriction cristallographique".
- 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 sameAs Q3527223.
- Crystallographic_restriction_theorem sameAs Crystallographic_restriction_theorem.
- Crystallographic_restriction_theorem wasDerivedFrom Crystallographic_restriction_theorem?oldid=604423001.
- Crystallographic_restriction_theorem depiction Crystallographic_restriction_polygons.png.
- Crystallographic_restriction_theorem isPrimaryTopicOf Crystallographic_restriction_theorem.