GroupTheory`
GroupTheory`

GTInstallGroup

GTInstallGroup[group]

gives a faithful representation of a crystallographic group.

Details and Options

  • Within GTPack the crystallographic point groups are implemented. According to GORepresentation, GTInstallGroup gives O(3) matrices for ordinary crystallographic point groups, SU(2) matrices for double groups without inversion, matrices of the outer direct product SU(2)x{1,-1} for double with inversion ("SU(2)xS"), as well as O(2) matrices for 2-dimensional point groups.
  • group can be a string or a symbol in Schönflies notation or a symbol in bracketing bars in Hermann–Mauguin notation.
  • Use GTGroupHierarchy to get an overview over all installed crystallographic point groups.
  • The palette contains all point group symbols and can be used to install the corresponding groups.
  • The following options can be given:
  • GORepresentation "O(3)"Defines the used standard representation
    GOVerbose TrueControls the output of additional information
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 3.1, 5.1.

Examples

open allclose all

Basic Examples  (2)

First, load the package:

Install the point group

Use Hermann–Mauguin notation

Install the space group Pm-3n

Install the space group Pm-3n using the space group number

Options  (6)

GOVerbose  (2)

GOVerbose False suppresses the text output.

GORepresentation  (4)

"O(3)" can be used for the installation of ordinary point groups

"O(2)" can be used for the installation of planar point groups

"SU(2)" can be used for the installation of double groups which do not contain the inversion.

"SU(2)xS" can be used for the installation of double groups which contain the inversion.

Possible Issues  (1)

If GORepresentation "SU(2)" is used for the installation of a point group containing the inversion, GTPack automatically switches to "SU(2)xS".