InternationalSpace-group symmetryTables for Crystallography Volume A Edited by M. I. Aroyo © International Union of Crystallography 2015 |
International Tables for Crystallography (2015). Vol. A, ch. 1.4, p. 48
## Section 1.4.1.4.7.2. Hexagonal space groups H. Wondratschek
^{e} |

Hexagonal space groups have either one or three representative symmetry directions. The space groups of crystal classes 6, and 6/*m* have [001] as their single symmetry direction for the axis 6 or 6_{k} for or , and for the plane *m* with its normal along [001]. The short and full HM symbols are the same. Examples are *P*6, , and .

Space groups of crystal classes 622, 6*mm*, and 6/*m*2/*m*2/*m* have the representative symmetry directions [001], [100] and . As opposed to the trigonal HM symbols, in the hexagonal HM symbols no symmetry direction is `empty' and occupied by `1'.

In space groups of the crystal classes 622, 6*mm* and the short and full HM symbols are the same; in 6/*m*2/*m*2/*m* the short symbols are deprived of the parts `2/' of the full symbols. The full HM symbol is shortened to the short HM symbol , the full HM symbol is shortened to . The two denote different space-group types.