(i) The pointgroup heading. This heading contains a short Hermann–Mauguin symbol of a point group, the crystal system and the symbol of the Laue group with which the point group is associated. Each pointgroup heading is followed by the set of space groups which are isomorphic to the point group indicated, the set being enclosed within a box.
(ii) The spacegroup heading. This heading contains, for each space group listed in Volume A (IT A, 1983), the short Hermann–Mauguin symbol of the space group, its conventional spacegroup number and (in parentheses) the serial number of its representation in Volume A; this is also the serial number of the explicit spacegroup symbol in Table A1.4.2.1 from which the entry was derived. Additional items are full spacegroup symbols, given only for the monoclinic space groups in their settings that are given in Volume A (IT, 1983), and selfexplanatory comments as required.
(iii) The table entry. In the context of the analysis in Section 1.4.2.2, the format of a table entry is: , where is the nth spacegroup operator, and the phase shift is expressed in units of 2π [see equations (1.4.2.3) and (1.4.2.5)]. More explicitly, the general format of a table entry isIn (1.4.4.1), n is the serial number of the spacegroup operation to which this entry pertains and is the same as the number of the general Wyckoff position generated by this operation and given in IT A (1983) for the space group appearing in the spacegroup heading. The first part of an entry, :, contains the coordinates of the reciprocallattice vector that was generated from the reference vector (hkl) by the rotation part of the nth spacegroup operation. These rotation parts of the table entries, for a given space group, thus constitute the set of reciprocallattice points that are generated by the corresponding point group (not Laue group). The second part of an entry is an abbreviation of the phase shift which is associated with the nth operation and thuswhere the fractions and are the components of the translation part of the nth spacegroup operation. The phaseshift part of an entry is given only if is not a vector in the direct lattice, since such a vector would give rise to a trivial phase shift (an integer multiple of 2π).
