It should be noted that some symmetry operations are purely translational while others while other operate referenced to a point, line or plane. When the symmetry operations for the space group do not have a specific reference to a location along each axis, then translating the coordinates along that axis leaves the structure unchanged. A space group that does not define an origin for x, y and z is called a polar space group. The polar space groups are all non-centrosymmetric because a center of symmetry defines an origin. Polar space groups can be discerned by looking the symmetry operations. Any operator that includes \(x^\prime = n-x\), will define an origin along a and so forth for b and c. It is important to recognize polar space groups as it is not possible to refine the coordinates for all atoms. As an example, in space group \(P 2_1\), the symmetry operations are x,y,z and -x,1/2+y,-z. This defines the origin with respect to a and c but not b. GSAS-II will note this when a polar space group is encountered, as noted in the text of Fig. 3.4.
