Section 2.2.6.6. Rhombohedral (trigonal R) space groups

The seven rhombohedral R space groups are treated in two versions, the first based on `hexagonal axes' (obverse setting), the second on `rhombohedral axes' (cf. Sections 2.1.3 and 2.2.2). The pairs of diagrams are similar to those in IT (1952); the left or top one displays the symmetry elements, the right or bottom one the general position. This is illustrated in Fig. 2.2.6.9, which gives the axes a and b of the triple hexagonal cell and the projections of the axes of the primitive rhombohedral cell, labelled and . For convenience, all `heights' in the space-group diagrams are fractions of the hexagonal c axis. For `hexagonal axes', the projection direction is [001], for `rhombohedral axes' it is [111]. In the general-position diagrams, the circles drawn in heavier lines represent atoms that lie within the primitive rhombohedral cell (provided the symbol `−' is read as rather than as ).

Figure 2.2.6.9| top | pdf | Rhombohedral R space groups. Obverse triple hexagonal cell with `hexagonal axes' a, b and primitive rhombohedral cell with projections of `rhombohedral axes' . Note: In the actual space-group diagrams only the upper edges (full lines), not the lower edges (dashed lines) of the primitive rhombohedral cell are shown ( = general-position diagram).

The pairs of drawings for the hexagonal and the rhombohedral descriptions of a space group are the same. In the rhombohedral descriptions of space groups Nos. 166 and 167, and , the diagrams are omitted for reasons of space, and the reader is referred to the drawings in the hexagonal descriptions.