Table 15.2.2.1

Koch, E.; Fischer, W.; Müller, U.

doi:10.1107/97809553602060000534

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. 15.2, p. 899

Table 15.2.2.1

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 15.2.2.1 | top | pdf |
Affine normalizers of the triclinic and monoclinic space groups

Space group $[{\cal G}]$		Matrix–vector pairs in Table 15.2.2.2
No.	Hermann–Mauguin symbol	Matrix–vector pairs in Table 15.2.2.2
1	P 1	$[{\bi M}_{1}, {\bi v}_{1}]$
2	$[P\bar{1}]$	$[{\bi M}_{1}, {\bi v}_{2}]$
3	P 121	$[{\bi M}_{2}, {\bi v}_{3}]$
3	P 112	$[{\bi M}_{3}, {\bi v}_{4}]$
4	$[P12_{1}1]$	$[{\bi M}_{2}, {\bi v}_{3}]$
4	$[P112_{1}]$	$[{\bi M}_{3}, {\bi v}_{4}]$
5	C 121	$[{\bi M}_{4}, {\bi v}_{3}]$
5	A 121	$[{\bi M}_{5}, {\bi v}_{3}]$
5	I 121	$[{\bi M}_{6}, {\bi v}_{3}\hbox{; } {\bi M}_{7}, {\bi v}_{3}]$
5	A 112	$[{\bi M}_{8}, {\bi v}_{4}]$
5	B 112	$[{\bi M}_{9}, {\bi v}_{4}]$
5	I 112	$[{\bi M}_{10}, {\bi v}_{4}\hbox{; } {\bi M}_{11}, {\bi v}_{4}]$
6	P 1m1	$[{\bi M}_{2}, {\bi v}_{5}]$
6	P 11m	$[{\bi M}_{3}, {\bi v}_{6}]$
7	P 1c1	$[{\bi M}_{5}, {\bi v}_{5}]$
7	P 1n1	$[{\bi M}_{6}, {\bi v}_{5}\hbox{; } {\bi M}_{7}, {\bi v}_{5}]$
7	P 1a1	$[{\bi M}_{4}, {\bi v}_{5}]$
7	P 11a	$[{\bi M}_{9}, {\bi v}_{6}]$
7	P 11n	$[{\bi M}_{10}, {\bi v}_{6}\hbox{; } {\bi M}_{11}, {\bi v}_{6}]$
7	P 11b	$[{\bi M}_{8}, {\bi v}_{6}]$
8	C 1m1	$[{\bi M}_{4}, {\bi v}_{5}]$
8	A 1m1	$[{\bi M}_{5}, {\bi v}_{5}]$
8	I 1m1	$[{\bi M}_{6}, {\bi v}_{5}\hbox{; } {\bi M}_{7}, {\bi v}_{5}]$
8	A 11m	$[{\bi M}_{8}, {\bi v}_{6}]$
8	B 11m	$[{\bi M}_{9}, {\bi v}_{6}]$
8	I 11m	$[{\bi M}_{10}, {\bi v}_{6}\hbox{; } {\bi M}_{11}, {\bi v}_{6}]$
9	C 1c1	$[{\bi M}_{6}, {\bi v}_{5}\hbox{; } {\bi M}_{12}, {\bi v}_{7}]$
9	A 1n1	$[{\bi M}_{6}, {\bi v}_{5}\hbox{; } {\bi M}_{13}, {\bi v}_{7}]$
9	I 1a1	$[{\bi M}_{6}, {\bi v}_{5}\hbox{; } {\bi M}_{7}, {\bi v}_{7}]$
9	A 11a	$[{\bi M}_{10}, {\bi v}_{6}\hbox{; } {\bi M}_{14}, {\bi v}_{8}]$
9	B 11n	$[{\bi M}_{10}, {\bi v}_{6}\hbox{; } {\bi M}_{15}, {\bi v}_{8}]$
9	I 11b	$[{\bi M}_{10}, {\bi v}_{6}\hbox{; } {\bi M}_{11}, {\bi v}_{8}]$
10	P 12/m1	$[{\bi M}_{2}, {\bi v}_{2}]$
10	P 112/m	$[{\bi M}_{3}, {\bi v}_{2}]$
11	$[P12_{1}/m1]$	$[{\bi M}_{2}, {\bi v}_{2}]$
11	$[P112_{1}/m]$	$[{\bi M}_{3}, {\bi v}_{2}]$
12	C 12/m1	$[{\bi M}_{4}, {\bi v}_{2}]$
12	A 12/m1	$[{\bi M}_{5}, {\bi v}_{2}]$
12	I 12/m1	$[{\bi M}_{6}, {\bi v}_{2}\hbox{; } {\bi M}_{7}, {\bi v}_{2}]$
12	A 112/m	$[{\bi M}_{8}, {\bi v}_{2}]$
12	B 112/m	$[{\bi M}_{9}, {\bi v}_{2}]$
12	I 112/m	$[{\bi M}_{10}, {\bi v}_{2}\hbox{; } {\bi M}_{11}, {\bi v}_{2}]$
13	P 12/c1	$[{\bi M}_{5}, {\bi v}_{2}]$
13	P 12/n1	$[{\bi M}_{6}, {\bi v}_{2}\hbox{; } {\bi M}_{7}, {\bi v}_{2}]$
13	P 12/a1	$[{\bi M}_{4}, {\bi v}_{2}]$
13	P 112/a	$[{\bi M}_{9}, {\bi v}_{2}]$
13	P 112/n	$[{\bi M}_{10}, {\bi v}_{2}\hbox{; } {\bi M}_{11}, {\bi v}_{2}]$
13	P 112/b	$[{\bi M}_{8}, {\bi v}_{2}]$
14	$[P12_{1}/c1]$	$[{\bi M}_{5}, {\bi v}_{2}]$
14	$[P12_{1}/n1]$	$[{\bi M}_{6}, {\bi v}_{2}\hbox{; } {\bi M}_{7}, {\bi v}_{2}]$
14	$[P12_{1}/a1]$	$[{\bi M}_{4}, {\bi v}_{2}]$
14	$[P112_{1}/a]$	$[{\bi M}_{9}, {\bi v}_{2}]$
14	$[P112_{1}/n]$	$[{\bi M}_{10}, {\bi v}_{2}\hbox{; } {\bi M}_{11}, {\bi v}_{2}]$
14	$[P112_{1}/b]$	$[{\bi M}_{8}, {\bi v}_{2}]$
15	C 12/c1	$[{\bi M}_{6}, {\bi v}_{2}\hbox{; } {\bi M}_{12}, {\bi v}_{9}]$
15	A 12/n1	$[{\bi M}_{6}, {\bi v}_{2}\hbox{; } {\bi M}_{13}, {\bi v}_{10}]$
15	I 12/a1	$[{\bi M}_{6}, {\bi v}_{2}\hbox{; } {\bi M}_{7}, {\bi v}_{11}]$
15	A 112/a	$[{\bi M}_{10}, {\bi v}_{2}\hbox{; } {\bi M}_{14}, {\bi v}_{10}]$
15	B 112/n	$[{\bi M}_{10}, {\bi v}_{2}\hbox{; } {\bi M}_{15}, {\bi v}_{12}]$
15	I 112/b	$[{\bi M}_{10}, {\bi v}_{2}\hbox{; } {\bi M}_{11}, {\bi v}_{11}]$