Table 11.2.2.2

Fischer, W.; Koch, E.

doi:10.1107/97809553602060000523

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. 11.2, p. 816

Table 11.2.2.2

W. Fischer^a and E. Koch^a ^*

^a Institut für Mineralogie, Petrologie und Kristallographie, Philipps-Universität, D-35032 Marburg, Germany
Correspondence e-mail: kochelke@mailer.uni-marburg.de

Table 11.2.2.2 | top | pdf |
Matrices for point-group symmetry operations and orientation of corresponding symmetry elements, referred to a hexagonal coordinate system (cf. Table 2.1.2.1 )

Symbol of symmetry operation and orientation of symmetry element	Transformed coordinates $[\tilde{x},\tilde{y},\tilde{z}]$	Matrix W	Symbol of symmetry operation and orientation of symmetry element	Transformed coordinates $[\tilde{x},\tilde{y},\tilde{z}]$	Matrix W	Symbol of symmetry operation and orientation of symmetry element	Transformed coordinates $[\tilde{x},\tilde{y},\tilde{z}]$	Matrix W
1		$[\pmatrix{1 &0 &0\cr 0 &1 &0\cr 0 &0 &1\cr}]$	$[\matrix{3^{+} {\hbox to 8pt{}}0,0,z\cr \cr{\hbox to 16pt{}}[001]\cr}]$	$[\bar{y},x - y,z]$	$[\pmatrix{0 &\bar{1} &0\cr 1 &\bar{1} &0\cr 0 &0 &1\cr}]$	$[\matrix{3^{-} {\hbox to 8pt{}}0,0,z\cr \cr{\hbox to 15.5pt{}}[001]\cr}]$	$[y - x,\bar{x},z]$	$[\pmatrix{\bar{1} &1 &0\cr \bar{1} &0 &0\cr 0 &0 &1\cr}]$
$[\matrix{2 {\hbox to 12pt{}}0,0,z\cr \cr{\hbox to 14pt{}}[001]\cr}]$	$[\bar{x},\bar{y},z]$	$[\pmatrix{\bar{1} &0 &0\cr 0 &\bar{1} &0\cr 0 &0 &1\cr}]$	$[\matrix{6^{+} {\hbox to 8pt{}}0,0,z\cr \cr{\hbox to 16pt{}}[001]\cr}]$		$[\pmatrix{1 &\bar{1} &0\cr 1 &0 &0\cr 0 &0 &1\cr}]$	$[\matrix{6^{-} {\hbox to 8pt{}}0,0,z\cr \cr{\hbox to 15.5pt{}}[001]\cr}]$		$[\pmatrix{0 &1 &0\cr \bar{1} &1 &0\cr 0 &0 &1\cr}]$
$[\matrix{2 {\hbox to 12pt{}}x,x,0\cr \cr{\hbox to 14pt{}}[110]\cr}]$	$[y,x,\bar{z}]$	$[\pmatrix{0 &1 &0\cr 1 &0 &0\cr 0 &0 &\bar{1}\cr}]$	$[\matrix{2 {\hbox to 14.5pt{}}x,0,0\cr \cr{\hbox to 15pt{}}[100]\cr}]$	$[x - y,\bar{y},\bar{z}]$	$[\pmatrix{1 &\bar{1} &0\cr 0 &\bar{1} &0\cr 0 &0 &\bar{1}\cr}]$	$[\matrix{2 {\hbox to 14pt{}}0,y,0\cr \cr{\hbox to 15pt{}}[010]\cr}]$	$[\bar{x},y - x,\bar{z}]$	$[\pmatrix{\bar{1} &0 &0\cr \bar{1} &1 &0\cr 0 &0 &\bar{1}\cr}]$
$[\matrix{2 {\hbox to 12pt{}}x,\bar{x},0\cr \cr{\hbox to 14pt{}}[1\bar{1}0]\cr}]$	$[\bar{y},\bar{x},\bar{z}]$	$[\pmatrix{0 &\bar{1} &0\cr \bar{1} &0 &0\cr 0 &0 &\bar{1}\cr}]$	$[\matrix{2 {\hbox to 14.5pt{}}x,2x,0\cr \cr{\hbox to 10.5pt{}}[120]\cr}]$	$[y - x,y,\bar{z}]$	$[\pmatrix{\bar{1} &1 &0\cr 0 &1 &0\cr 0 &0 &\bar{1}\cr}]$	$[\matrix{2 {\hbox to 14pt{}}2x,x,0\cr \cr{\hbox to 10.5pt{}}[210]\cr}]$	$[x,x - y,\bar{z}]$	$[\pmatrix{1 &0 &0\cr 1 &\bar{1} &0\cr 0 &0 &\bar{1}\cr}]$
$[\matrix{\bar{1} {\hbox to 12pt{}}0,0,0\cr}]$	$[\bar{x},\bar{y},\bar{z}]$	$[\pmatrix{\bar{1} &0 &0\cr 0 &\bar{1} &0\cr 0 &0 &\bar{1}\cr}]$	$[\matrix{\bar{3}^{+} {\hbox to 8pt{}}0,0,z\cr \cr{\hbox to 16pt{}}[001]\cr}]$	$[y,y - x,\bar{z}]$	$[\pmatrix{0 &1 &0\cr \bar{1} &1 &0\cr 0 &0 &\bar{1}\cr}]$	$[\matrix{\bar{3}^{-} {\hbox to 8pt{}}0,0,z\cr \cr{\hbox to 16pt{}}[001]\cr}]$	$[x - y,x,\bar{z}]$	$[\pmatrix{1 &\bar{1} &0\cr 1 &0 &0\cr 0 &0 &\bar{1}\cr}]$
$[\matrix{m {\hbox to 10pt{}}x,y,0\cr \cr{\hbox to 13.5pt{}}[001]\cr}]$	$[x,y,\bar{z}]$	$[\pmatrix{1 &0 &0\cr 0 &1 &0\cr 0 &0 &\bar{1}\cr}]$	$[\matrix{\bar{6}^{+} {\hbox to 8pt{}}0,0,z\cr \cr{\hbox to 16pt{}}[001]\cr}]$	$[y - x,\bar{x},\bar{z}]$	$[\pmatrix{\bar{1} &1 &0\cr \bar{1} &0 &0\cr 0 &0 &\bar{1}\cr}]$	$[\matrix{\bar{6}^{-} {\hbox to 8pt{}}0,0,z\cr \cr{\hbox to 15.5pt{}}[001]\cr}]$	$[\bar{y},x - y,\bar{z}]$	$[\pmatrix{0 &\bar{1} &0\cr 1 &\bar{1} &0\cr 0 &0 &\bar{1}\cr}]$
$[\matrix{m {\hbox to 10pt{}}x,\bar{x},z\cr \cr{\hbox to 14.5pt{}}[110]\cr}]$	$[\bar{y},\bar{x},z]$	$[\pmatrix{0 &\bar{1} &0\cr \bar{1} &0 &0\cr 0 &0 &1\cr}]$	$[\matrix{m {\hbox to 12pt{}}x,2x,z\cr \cr{\hbox to 12pt{}}[100]\cr}]$		$[\pmatrix{\bar{1} &1 &0\cr 0 &1 &0\cr 0 &0 &1\cr}]$	$[\matrix{m {\hbox to 12pt{}}2x,x,z\cr \cr{\hbox to 11.5pt{}}[010]\cr}]$		$[\pmatrix{1 &0 &0\cr 1 &\bar{1} &0\cr 0 &0 &1\cr}]$
$[\matrix{m {\hbox to 10pt{}}x,x,z\cr \cr{\hbox to 14.5pt{}}[1\bar{1}0]\cr}]$		$[\pmatrix{0 &1 &0\cr 1 &0 &0\cr 0 &0 &1\cr}]$	$[\matrix{m {\hbox to 12pt{}}x,0,z\cr \cr{\hbox to 16.5pt{}}[120]\cr}]$	$[x - y,\bar{y},z]$	$[\pmatrix{1 &\bar{1} &0\cr 0 &\bar{1} &0\cr 0 &0 &1\cr}]$	$[\matrix{m {\hbox to 12pt{}}0,y,z\cr \cr{\hbox to 16pt{}}[210]\cr}]$	$[\bar{x},y - x,z]$	$[\pmatrix{\bar{1} &0 &0\cr \bar{1} &1 &0\cr 0 &0 &1\cr}]$