International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 2.1, p. 157

## Section 2.1.3.6.6. Trigonal R (rhombohedral) space groups

Th. Hahna and A. Looijenga-Vosb

#### 2.1.3.6.6. Trigonal R (rhombohedral) space groups

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The seven rhombohedral space groups are treated in two versions, the first based on hexagonal axes' (obverse setting), the second on rhombohedral axes' (cf. Sections 2.1.1.2 and 2.1.3.2). The pairs of diagrams are similar to those in IT (1952) and IT A (2002); the left or top one displays the symmetry elements, the right or bottom one the general position. This is illustrated in Fig. 2.1.3.9, which gives the axes a and b of the triple hexagonal cell and the projections of the axes of the primitive rhombohedral cell, labelled arh, brh and crh. 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 2.1.3.9 | top | pdf |Rhombohedral space groups. Obverse triple hexagonal cell with hexagonal axes' a, b and primitive rhombohedral cell with projections of rhombohedral axes' arh, brh, crh. Note: In the actual space-group diagrams the edges of the primitive rhombohedral cell (dashed lines) are only indicated in the general-position diagram of the rhombohedral-axes description ( = general-position diagram).

The symmetry-element diagrams for the hexagonal and the rhombohedral descriptions of a space group are the same. The edges of the primitive rhombohedral cell (cf. Fig. 2.1.3.9) are only indicated in the general-position diagram of the rhombohedral description.

### References

International Tables for Crystallography (2002). Vol. A, 5th ed., edited by Th. Hahn. Dordrecht: Kluwer Academic Publishers. [Abbreviated as IT A (2002).]
International Tables for X-ray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press. [Revised editions: 1965, 1969 and 1977. Abbreviated as IT (1952).]