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Symmetry Operations of Crystallographic Point Groups and Space Groups

Wang Xianlong
Organization: Max Planck Institute for Chemical Physics of Solids
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There are 32 crystallographic point groups and 230 space groups in three-dimensional space. Symmetry operations of them are given in the vector form in this notebook. For the space groups, both the operations for general positions and for the unique generators are included. A function to convert the vector form to the affine matrix form is given. The affine matrix consists of the transformation matrix and the shift vector. An additional function is written to give the transformation matrix only if the shift is unnecessary, i.e. the shift vector={0,0,0}. In chemistry and physics, it is interesting sometimes to know whether a point group is contained in some space groups. A short script has been written to generate the correspondence table between the two.

*Science > Chemistry
*Science > Physics > Crystallography

Crystallographic Point Groups, Space Groups, Symmetry Operations
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CrystalPointSpaceGroups.nb (237.8 KB) - Mathematica Notebook [for Mathematica 5.2]