Table 15.2.2.2

Koch, E.; Fischer, W.; Müller, U.

doi:10.1107/97809553602060000534

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

pdf | chapter contents | chapter index | related articles

International Tables for Crystallography (2006). Vol. A. ch. 15.2, p. 899

Table 15.2.2.2

E. Koch,^a ^* W. Fischer^a and U. Müller^b

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

Table 15.2.2.2 | top | pdf |
Matrices and vectors used in Table 15.2.2.1 for the description of the affine normalizers of monoclinic and triclinic space groups

n , g and u represent integer, even and odd numbers, respectively, r, s and t real numbers. For all matrices, $[\det ({\bi M}_{i}) = \pm 1]$ must hold.

$[{\bi M}_{1} =\pmatrix{n_{11}\hfill &n_{12}\hfill &n_{13}\hfill\cr n_{21}\hfill &n_{22}\hfill &n_{23}\hfill\cr n_{31}\hfill &n_{32}\hfill &n_{33}\hfill\cr}]$	$[{\bi M}_{2} =\pmatrix{n_{11}\hfill &0\hfill &n_{13}\hfill\cr 0\hfill &\pm 1\hfill &0\hfill\cr n_{31}\hfill &0\hfill &n_{33}\hfill\cr}]$	$[{\bi M}_{3} =\pmatrix{n_{11}\hfill &n_{12}\hfill &0\hfill\cr n_{21}\hfill &n_{22}\hfill &0\hfill\cr 0\hfill &0\hfill &\pm 1\hfill\cr}]$	$[{\bi M}_{4} =\pmatrix{u_{11}\hfill &0\hfill &n_{13}\hfill\cr 0\hfill &\pm 1\hfill &0\hfill\cr g_{31}\hfill &0\hfill &u_{33}\hfill\cr}]$	$[{\bi M}_{5} =\pmatrix{u_{11}\hfill &0\hfill &g_{13}\hfill\cr 0\hfill &\pm 1\hfill &0\hfill\cr n_{31}\hfill &0\hfill &u_{33}\hfill\cr}]$
$[{\bi M}_{6} =\pmatrix{u_{11}\hfill &0\hfill &g_{13}\hfill\cr 0\hfill &\pm 1\hfill &0\hfill\cr g_{31}\hfill &0\hfill &u_{33}\hfill\cr}]$	$[{\bi M}_{7} =\pmatrix{g_{11}\hfill &0\hfill &u_{13}\hfill\cr 0\hfill &\pm 1\hfill &0\hfill\cr u_{31}\hfill &0\hfill &g_{33}\hfill\cr}]$	$[{\bi M}_{8} =\pmatrix{u_{11}\hfill &g_{12}\hfill &0\hfill\cr n_{21}\hfill &u_{22}\hfill &0\hfill\cr 0\hfill &0\hfill &\pm 1\hfill\cr}]$	$[{\bi M}_{9} =\pmatrix{u_{11}\hfill &n_{12}\hfill &0\hfill\cr g_{21}\hfill &u_{22}\hfill &0\hfill\cr 0\hfill &0\hfill &\pm 1\hfill\cr}]$	$[{\bi M}_{10} =\pmatrix{u_{11}\hfill &g_{12}\hfill &0\hfill\cr g_{21}\hfill &u_{22}\hfill &0\hfill\cr 0\hfill &0\hfill &\pm 1\hfill\cr}]$
$[{\bi M}_{11} =\pmatrix{g_{11}\hfill &u_{12}\hfill &0\hfill\cr u_{21}\hfill &g_{22}\hfill &0\hfill\cr 0\hfill &0\hfill &\pm 1\hfill\cr}]$	$[{\bi M}_{12} =\pmatrix{u_{11}\hfill &0\hfill &u_{13}\hfill\cr 0\hfill &\pm 1\hfill &0\hfill\cr g_{31}\hfill &0\hfill &u_{33}\hfill\cr}]$	$[{\bi M}_{13} =\pmatrix{u_{11}\hfill &0\hfill &g_{13}\hfill\cr 0\hfill &\pm 1\hfill &0\hfill\cr u_{31}\hfill &0\hfill &u_{33}\hfill\cr}]$	$[{\bi M}_{14} =\pmatrix{u_{11}\hfill &g_{12}\hfill &0\hfill\cr u_{21}\hfill &u_{22}\hfill &0\hfill\cr 0\hfill &0\hfill &\pm 1\hfill\cr}]$	$[{\bi M}_{15} =\pmatrix{u_{11}\hfill &u_{12}\hfill &0\hfill\cr g_{21}\hfill &u_{22}\hfill &0\hfill\cr 0\hfill &0\hfill &\pm 1\hfill\cr}]$
$[\openup2.5pt {\bi v}_{1} =\pmatrix{r\hfill\cr s\hfill\cr t\hfill\cr}]$	$[\openup2.5pt {\bi v}_{2} =\pmatrix{{1 \over 2}n_{1}\hfill\cr {1 \over 2}n_{2}\hfill\cr {1 \over 2}n_{3}\hfill\cr}]$	$[\openup2.5pt {\bi v}_{3} =\pmatrix{{1 \over 2}n_{1}\hfill\cr s\hfill\cr {1 \over 2}n_{3}\hfill\cr}]$	$[\openup2.5pt {\bi v}_{4} =\pmatrix{{1 \over 2}n_{1}\hfill\cr {1 \over 2}n_{2}\hfill\cr t\hfill\cr}]$	$[\openup2.5pt {\bi v}_{5} =\pmatrix{r\hfill\cr {1 \over 2}n_{2}\hfill\cr t\hfill\cr}]$
$[\openup2.5pt {\bi v}_{6} =\pmatrix{r\hfill\cr s\hfill\cr {1 \over 2}n_{3}\hfill\cr}]$	$[\openup2.5pt {\bi v}_{7} =\pmatrix{r\hfill\cr {1 \over 4}u_{2}\hfill\cr t\hfill\cr}]$	$[\openup2.5pt {\bi v}_{8} =\pmatrix{r\hfill\cr s\hfill\cr {1 \over 4}u_{3}\hfill\cr}]$	$[\openup2.5pt {\bi v}_{9} =\pmatrix{{1 \over 4}u_{1}\hfill\cr {1 \over 4}u_{2}\hfill\cr {1 \over 2}n_{3}\hfill\cr}]$	$[\openup2.5pt {\bi v}_{10} =\pmatrix{{1 \over 2}n_{1}\hfill\cr {1 \over 4}u_{2}\hfill\cr {1 \over 4}u_{3}\hfill\cr}]$
$[\openup2.5pt {\bi v}_{11} =\pmatrix{{1 \over 4}u_{1}\hfill\cr {1 \over 4}u_{2}\hfill\cr {1 \over 4}u_{3}\hfill\cr}]$	$[\openup2.5pt {\bi v}_{12} =\pmatrix{{1 \over 4}u_{1}\hfill\cr {1 \over 2}n_{2}\hfill\cr {1 \over 4}u_{3}\hfill\cr}]$