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

International Tables for Crystallography (2015). Vol. A, ch. 1.4, p. 59


H. Wondratscheke

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Sequence of generators for the crystal classes

The space-group generators differ from those listed here by their glide or screw components. The generator 1 is omitted, except for crystal class 1. The generators are represented by the corresponding Seitz symbols (cf. Tables[link] –[link] ). Following the conventions, the subscript of a symbol denotes the characteristic direction of that operation, where necessary. For example, the subscripts 001, 010, 110 etc. refer to the directions [001], [010], [110] etc. For mirror reflections m, the `direction of m' refers to the normal of the mirror plane.

Hermann–Mauguin symbol of crystal classGenerators [\ispecialfonts{\sfi g}_{i}] (sequence left to right)
1 1
[\bar{1}] [\bar{1}]
2 2
m m
[2/m] [2,\bar{1}]
222 [2_{001},2_{010}]
mm2 [2_{001},m_{010}]
mmm [2_{001},2_{010},\bar{1}]
4 [2_{001},4^+_{001}]
[\bar{4}] [2_{001},\bar{4}^+_{001}]
[4/m] [2_{001},4^+_{001},\bar{1}]
422 [2_{001},4^+_{001},2_{010}]
4mm [2_{001},4^+_{001},m_{010}]
[\bar{4}2m] [2_{001},\bar{4}^+_{001},2_{010}]
[\bar{4}m2] [2_{001},\bar{4}^+_{001},m_{010}]
[4/mmm] [2_{001},4^+_{001},2_{010},\bar{1}]
3 [3^+_{001}]
(rhombohedral coordinates [3^+_{111}])
[\bar{3}] [3^+_{001},\bar{1}]
(rhombohedral coordinates [3^+_{111},\bar{1}]
321 [3^+_{001},2_{110}]
(rhombohedral coordinates [3^+_{111},2_{\bar{1}01}])
312 [3^+_{001},2_{1\bar{1}0}]
3m1 [3^+_{001},m_{110}]
(rhombohedral coordinates [3^+_{111},m_{\bar{1}01}])
31m [3^+_{001},m_{1\bar{1}0}]
[\bar{3}m1] [3^+_{001},2_{110},\bar{1}]
(rhombohedral coordinates [3^+_{111},2_{\bar{1}01},\bar{1}])
[\bar{3}1m] [3^+_{001},2_{1\bar{1}0},\bar{1}]
6 [3^+_{001},2_{001}]
[\bar{6}] [3^+_{001},m_{001}]
[6/m] [3^+_{001},2_{001},\bar{1}]
622 [3^+_{001},2_{001},2_{110}]
6mm [3^+_{001},2_{001},m_{110}]
[\bar{6}m2] [3^+_{001},m_{001},m_{110}]
[\bar{6}2m] [3^+_{001},m_{001},2_{110}]
[6/mmm] [3^+_{001},2_{001},2_{110},\bar{1}]
23 [2_{001},2_{010},3^+_{111}]
[m\bar{3}] [2_{001},2_{010},3^+_{111},\bar{1}]
432 [2_{001},2_{010},3^+_{111},2_{110}]
[\bar{4}3m] [2_{001},2_{010},3^+_{111},m_{1\bar{1}0}]
[m\bar{3}m] [2_{001},2_{010},3^+_{111},2_{110},\bar{1}]