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

International Tables for Crystallography (2016). Vol. A, ch. 3.3, p. 778


H. Burzlaffa and H. Zimmermannb*

aUniversität Erlangen–Nürnberg, Robert-Koch-Strasse 4a, D-91080 Uttenreuth, Germany, and bInstitut für Angewandte Physik, Lehrstuhl für Kristallographie und Strukturphysik, Universität Erlangen–Nürnberg, Bismarckstrasse 10, D-91054 Erlangen, Germany
Correspondence e-mail:

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Representatives for the sets of lattice symmetry directions in the various crystal families

Crystal familyAnorthic (triclinic)MonoclinicOrthorhombicTetragonalHexagonalCubic
Lattice point group Schoenflies [C_{i}] [C_{2h}] [D_{2h}] [D_{4h}] [D_{6h}] [D_{3d}] [O_{h}]
Hermann–Mauguin [\bar{1}] [\displaystyle{2 \over m}] [\displaystyle{2 \over m} {2 \over m} {2 \over m}] [\displaystyle{4 \over m} {2 \over m} {2 \over m}] [\displaystyle{6 \over m} {2 \over m} {2 \over m}] [\displaystyle\bar{3} {2 \over m}] [\displaystyle{4 \over m} \bar{3} {2 \over m}]
Set of lattice symmetry directions Primary [010]          
b unique [100] [001] [001] [001] [001]
c unique          
Secondary [010] [100] [100] [100] [111]
Tertiary [001] [\hbox{[}1\bar{1}0\hbox{]}] [\hbox{[}1\bar{1}0\hbox{]}] [\hbox{[}1\bar{1}0\hbox{]}]
In this table, the directions refer to the hexagonal description. The use of the primitive rhombohedral cell brings out the relations between cubic and rhombohedral groups: the primary set is represented by [111] and the secondary by [[1\bar 10]].
Only for [\bar{4}3m] and 432 [for reasons see text].