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

International Tables for Crystallography (2016). Vol. A, ch. 1.6, p. 123

Table 1.6.4.22 

H. D. Flackb and U. Shmuelia

Table 1.6.4.22| top | pdf |
Reflection conditions and possible space groups with Bravais lattice hR and Laue class [\overline{3}m] (hexagonal axes); hki are permutable; Patterson symmetry [R\overline{3}m]; Ov = obverse setting; Rv = reverse setting

Reflection conditionsSpace groupNo.Space groupNo.Space groupNo. 
[hkil][hki0][hh\overline{2h}l][h\overline{h}0l][000l][h\overline{h}00]
[-h+k+l=3n] [-h+k=3n] [l=3n] [h+l=3n] [l=3n] [h=3n] R32 155 [R3m] 160 [R\overline{3}m] 166 Ov
                         
[-h+k+l=3n] [-h+k=3n] [l=3n] [h+l=3n], [l=2m] [l=6n] [h=3n] [R3c] 161 [R\overline{3}c] 167     Ov
                         
[h-k+l=3n] [h-k=3n] [l=3n] [-h+l=3n] [l=3n] [h=3n] R32 155 [R3m] 160 [R\overline{3}m] 166 Rv
                         
[h-k+l=3n] [h-k=3n] [l=3n] [-h+l=3n,l=2m] [l=6n] [h=3n] [R3c] 161 [R\overline{3}c] 167     Rv