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- Q3527223 subject Q7139579.
- Q3527223 subject Q7217286.
- Q3527223 subject Q7464146.
- Q3527223 subject Q8266681.
- Q3527223 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.".
- Q3527223 thumbnail Crystallographic_restriction_polygons.png?width=300.
- Q3527223 wikiPageExternalLink digbib.cgi?PPN378850199_0001.
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- Q3527223 wikiPageExternalLink 42.pdf.
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- Q3527223 wikiPageWikiLink Q7217286.
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- Q3527223 wikiPageWikiLink Q7464146.
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- Q3527223 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).".
- Q3527223 label "Crystallographic restriction theorem".
- Q3527223 depiction Crystallographic_restriction_polygons.png.