Table 4.1.2.1

Bertaut, E. F.

doi:10.1107/97809553602060000507

International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by Th. Hahn

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International Tables for Crystallography (2006). Vol. A. ch. 4.1, p. 57

Table 4.1.2.1

E. F. Bertaut^a ^‡

^a Laboratoire de Cristallographie, CNRS, Grenoble, France

Table 4.1.2.1 | top | pdf |
Location of additional symmetry element, if the translation vector t is perpendicular to the symmetry axis along [0,0,z] or to the symmetry plane in [x,y,0]

The symmetry centre at 0, 0, 0 is included. The table is restricted to integral translations (for centring translations, see Table 4.1.2.3). The symbol ↺ indicates cyclic permutation.

Symmetry element at the origin	Translation vector t	Location of additional symmetry element	Representative plane and space groups (numbers)
$[2,2_{1}]$	1, 0, 0	$[{1 \over 2},0,z]$	$[P2\;(3), P2_{1}\;(4), p2\;(2)]$
	0, 1, 0	$[0,{1 \over 2},z]$
	1, 1, 0	$[{1 \over 2},{1 \over 2},z]$
$[3,3_{1},3_{2}]$	1, 0, 0	$[{2 \over 3},{1 \over 3},z]$	$[P3\;(143)\hbox{--}P3_{2}\;(145), p3\;(13)]$
$[3,3_{1},3_{2}]$	1, 1, 0	$[{1 \over 3},{2 \over 3},z]$
$[4,4_{1},4_{2},4_{3}]$	1, 0, 0	$[{1 \over 2},{1 \over 2},z]$	$[P4\;(75)\hbox{--}P4_{3}\ (78), p4(10)]$
$[6,6_{1},6_{2},6_{3},6_{4},6_{5}]$	–	–	$[P6\;(168)\hbox{--}P6_{5}\;(173), p6\;(16)]$
m, a, b, n, d, e	0, 0, 1	$[x,y,{1 \over 2}]$	$[Pm\ (6), Pa, Pb, Pn\ (7), Fddd\ (70), Cmme \ (67)]$
$[\bar{1}]$	1, 0, 0 ↺	$[{1 \over 2},0,0]$ ↺	$[P\bar{1}]$ (2)
	1, 1, 0 ↺	$[{1 \over 2},{1 \over 2},0]$ ↺
	1, 1, 1	$[{1 \over 2},{1 \over 2},{1 \over 2}]$
$[\bar{3}]$	–	–	$[P\bar{3}]$ (147)
$[\bar{4}]$	0, 1, 0	$[{1 \over 2}, {1 \over 2}, z]$	$[P\bar{4}]$ (81)
$[\bar{6}]$	0, 1, 0	$[{1 \over 3}, {2 \over 3}, z]$	$[P\bar{6}]$ (174)
$[\bar{6}]$	1, 1, 0	$[{2 \over 3}, {1 \over 3}, z]$