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

International Tables for Crystallography (2015). Vol. A, ch. 1.4, p. 48

Section 1.4.1.4.7.2. Hexagonal space groups

H. Wondratscheke

1.4.1.4.7.2. Hexagonal space groups

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Hexagonal space groups have either one or three representative symmetry directions. The space groups of crystal classes 6, [\overline{6}] and 6/m have [001] as their single symmetry direction for the axis 6 or 6k for [k=1,\ldots, 5] or [\overline{6}], and for the plane m with its normal along [001]. The short and full HM symbols are the same. Examples are P6, [P6_4], [P\overline{6}] and [P6_3/m].

Space groups of crystal classes 622, 6mm, [\overline{6}2m] and 6/m2/m2/m have the representative symmetry directions [001], [100] and [[1\overline{1}0]]. 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, 6mm and [\overline{6}2m] the short and full HM symbols are the same; in 6/m2/m2/m the short symbols are deprived of the parts `2/' of the full symbols. The full HM symbol [P\,6_3/m\,2/m\,2/c] is shortened to the short HM symbol [P6_3/mmc], the full HM symbol [P\,6_3/m\,2/c\,2/m] is shortened to [P6_3/mcm]. The two denote different space-group types.








































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