$PointGroups

$PointGroups
is an association containing data on the 32 crystallographic point groups.

DetailsDetails

  • The Keys of $PointGroups are the (formatted) symbols of the corresponding point group and the Values are themselves associations organised in the following structure:
  • Symbol (Full symbol) Point group number Crystal system Laue class Schoenflies symbol Setting Class names     Groth     Friedel         (Hexaognal)         (Rhombohedral) Properties     Centrosymmetric?     Enantiomorphic?     Polar? Symmetry operations     Matrix operations     Symmetry operation (ITA notation)     Symmetry operation (Setiz notation) Subgroups     {      Subgroup class type      Subgroup symmetry      Subgroup list     }
  • Entries in parentheses are only present where applicable.
  • Some point groups may have multiple representations (various choices of unique axis, orientation of symmetry elements, rhombohedral axes). This information is stored in an additional sub-assoociation;
  • Alternative settings     Symbol     (Full symbol)     (Full symbol, alternative postfix)     (Symbol, alternative postfix)     (Symbol, plain string)     (Symbol, plain string, alternative postfix)     (Full symbol, plain string)     (Full symbol, plain string, alternative postfix)     Setting     Symmetry operations              Subgroups         
  • Entries in parentheses are only present where applicable.
  • Although point groups do not have a «point group number» associated with them like the space groups, they have been attributed one here to arrange them in canonical order.
  • The "ClassNames" data is found in table 10.1.2.4 on page 794 in International Tables for Crystallography,volume A [1]
  • $PointGroups is loaded from:
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ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

The association has 32 point group entries, arranged from least to highest symmetry.

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The desired information can be extracted easily:

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