Space-Group Symbols

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Short Space-Group Symbol

The short space-group symbol is written in the top left-hand corner of each space-group diagram and on each of the pages associated with that diagram. Reflection conditions associated with the space group for atoms on general positions x,y,z may be derived from this short space-group symbol. Note that for many space groups, the short space-group symbol and the full space-group symbol are identical.

The shortened form leaves out symmetry elements that are implicitly present: For example, the orthorhombic space group Pbca implicitly has three two-one screw axes due to the presence of the three mutually-perpendicular glide planes. These two-one axes are omitted from the short symbol, but retained in the full symbol.

Full Space-Group Symbol

The full space group symbol is shown after the short space-group symbol on the top line of the space-group diagrams. For monoclinic space groups, the full symbol emphasizes the unique axis direction. For centrosymmetric space groups associated with any of the point groups mmm, 4/mmm, -3m, 6/mmm, m-3, and m-3m, the full space-group symbol emphasizes the presence of rotation and screw axes not shown in the short space-group symbol.

Extended Space-Group Symbol

For centred space groups, extended space group symbols exist. These have not been given in this hypertext book. Typically, the extended symbol emphasizes additional symmetry elements implicitly present as a result of choosing a centred lattice: For example, the space group C1c1 possesses both c- and n-glide planes with the space group symbol showing only the former. By writing an "n" below the letter "c", the extended symbol emphasizes the existence of both glide planes.

For further information on the actual notation used, click here.

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