Table 15.2.1.4

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, pp. 895-898

Table 15.2.1.4

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 15.2.1.4 | top | pdf |
Euclidean normalizers of the tetragonal, trigonal, hexagonal and cubic space groups

The symbols in parentheses following a space-group symbol refer to the location of the origin (`origin choice' in Part 7 ).

Space group $[{\cal G}]$		Euclidean normalizer $[{\cal N}\!_{{\cal E}}({\cal G})]$		Additional generators of $[{\cal N}\!_{{\cal E}}({\cal G})]$			Index of $[{\cal G}]$ in $[{\cal N}\!_{{\cal E}}({\cal G})]$
No.	Hermann–Mauguin symbol	Symbol	Basis vectors	Translations	Inversion through a centre at	Further generators
75	P 4	$[P^{1}4/mmm]$	$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), \varepsilon {\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ;	0, 0, 0	y , x, z	$[(2\cdot \infty)\cdot 2\cdot 2]$
76	$[P4_{1}]$	$[P^{1}422]$	$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), \varepsilon {\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ;	/		$[(2\cdot \infty)\cdot 2]$
77	$[P4_{2}]$	$[P^{1}4/mmm]$	$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), \varepsilon {\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ;	0, 0, 0	y , x, z	$[(2\cdot \infty)\cdot 2\cdot 2]$
78	$[P4_{3}]$	$[P^{1}422]$	$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), \varepsilon {\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ;	/		$[(2\cdot \infty)\cdot 2]$
79	I 4	$[P^{1}4/mmm]$	$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), \varepsilon {\bf c}]$	0, 0, t	0, 0, 0	y , x, z	$[\infty \cdot 2\cdot 2]$
80	$[I4_{1}]$	$[P^{1}4/nbm\ (\bar{4}2m)]$	$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), \varepsilon {\bf c}]$	0, 0, t	$[{1 \over 4},0, 0]$		$[\infty \cdot 2\cdot 2]$
81	$[P\bar{4}]$		$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0	y , x, z	$[4\cdot 2\cdot 2]$
82	$[I\bar{4}]$		$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},0,{1 \over 4}]$	0, 0, 0	y , x, z	$[4\cdot 2\cdot 2]$
83			$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$		y , x, z	$[4\cdot 1\cdot 2]$
84	$[P4_{2}/m]$		$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$		y , x, z	$[4\cdot 1\cdot 2]$
85	$[P4/n\ (\bar{4})]$		$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$		y , x, z	$[4\cdot 1\cdot 2]$
85	$[P4/n\ (\bar{1})]$	$[P4/mmm\ (mmm)]$	$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$		y , x, z	$[4\cdot 1\cdot 2]$
86	$[P4_{2}/n\ (\bar{4})]$		$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$		y , x, z	$[4\cdot 1\cdot 2]$
86	$[P4_{2}/n\ (\bar{1})]$	$[P4/mmm\ (mmm)]$	$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$		y , x, z	$[4\cdot 1\cdot 2]$
87			$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), {1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$		y , x, z	$[2\cdot 1\cdot 2]$
88	$[I4_{1}/a\ (\bar{4})]$	$[P4_{2}/nnm\ (\bar{4}2m)]$	$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), {1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 2]$
88	$[I4_{1}/a\ (\bar{1})]$	$[P4_{2}/nnm\ (2/m)]$	$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), {1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$		$[y + {1 \over 4}]$ , $[x + {1 \over 4}]$ , $[z + {1 \over 4}]$	$[2\cdot 1\cdot 2]$
89	P 422		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
90	$[P42_{1}2]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
91	$[P4_{1}22]$	$[\displaylines{P4_{2}22\ (222)\hfill\cr\hbox{origin at}\ 4_{2}12\hfill}]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	/		$[4\cdot 1]$
92	$[P4_{1}2_{1}2]$	$[P4_{2}22]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	/		$[4\cdot 1]$
93	$[P4_{2}22]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
94	$[P4_{2}2_{1}2]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
95	$[P4_{3}22]$	$[\displaylines{P4_{2}22\ (222)\hfill\cr\hbox{origin at}\ 4_{2}12\hfill}]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	/		$[4\cdot 1]$
96	$[P4_{3}2_{1}2]$	$[P4_{2}22]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	/		$[4\cdot 1]$
97	I 422		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	0, 0, 0		$[2\cdot 2\cdot 1]$
98	$[I4_{1}22]$	$[P4_{2}/nnm\ (\bar{4}2m)]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	$[{1 \over 4},0,{1 \over 8}]$		$[2\cdot 2\cdot 1]$
99	P 4mm	$[P^{1}4/mmm]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), \varepsilon {\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ;	0, 0, 0		$[(2\cdot \infty)\cdot 2\cdot 1]$
100	P 4bm	$[P^{1}4/mmm]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), \varepsilon {\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ;	0, 0, 0		$[(2\cdot \infty)\cdot 2\cdot 1]$
101	$[P4_{2}cm]$	$[P^{1}4/mmm]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), \varepsilon {\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ;	0, 0, 0		$[(2\cdot \infty)\cdot 2\cdot 1]$
102	$[P4_{2}nm]$	$[P^{1}4/mmm]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), \varepsilon {\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ;	0, 0, 0		$[(2\cdot \infty)\cdot 2\cdot 1]$
103	P 4cc	$[P^{1}4/mmm]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), \varepsilon {\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ;	0, 0, 0		$[(2\cdot \infty)\cdot 2\cdot 1]$
104	P 4nc	$[P^{1}4/mmm]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), \varepsilon {\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ;	0, 0, 0		$[(2\cdot \infty)\cdot 2\cdot 1]$
105	$[P4_{2}mc]$	$[P^{1}4/mmm]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), \varepsilon {\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ;	0, 0, 0		$[(2\cdot \infty)\cdot 2\cdot 1]$
106	$[P4_{2}bc]$	$[P^{1}4/mmm]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), \varepsilon {\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ;	0, 0, 0		$[(2\cdot \infty)\cdot 2\cdot 1]$
107	I 4mm	$[P^{1}4/mmm]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), \varepsilon {\bf c}]$	0, 0, t	0, 0, 0		$[\infty \cdot 2\cdot 1]$
108	I 4cm	$[P^{1}4/mmm]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), \varepsilon {\bf c}]$	0, 0, t	0, 0, 0		$[\infty \cdot 2\cdot 1]$
109	$[I4_{1}md]$	$[P^{1}4/nbm\ (\bar{4}2m)]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), \varepsilon {\bf c}]$	0, 0, t	$[{1 \over 4},0, 0]$		$[\infty \cdot 2\cdot 1]$
110	$[I4_{1}cd]$	$[P^{1}4/nbm\ (\bar{4}2m)]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), \varepsilon {\bf c}]$	0, 0, t	$[{1 \over 4},0, 0]$		$[\infty \cdot 2\cdot 1]$
111	$[P\bar{4}2m]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
112	$[P\bar{4}2c]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
113	$[P\bar{4}2_{1}m]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
114	$[P\bar{4}2_{1}c]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
115	$[P\bar{4}m2]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
116	$[P\bar{4}c2]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
117	$[P\bar{4}b2]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
118	$[P\bar{4}n2]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
119	$[I\bar{4}m2]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},0,{1 \over 4}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
120	$[I\bar{4}c2]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},0,{1 \over 4}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
121	$[I\bar{4}2m]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	0, 0, 0		$[2\cdot 2\cdot 1]$
122	$[I\bar{4}2d]$	$[P4_{2}/nnm\ (\bar{4}2m)]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	$[{1 \over 4},0,{1 \over 8}]$		$[2\cdot 2\cdot 1]$
123			$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
124			$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
125	$[P4/nbm\ (422)]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
125	$[P4/nbm\ (2/m)]$	$[P4/mmm\ (mmm)]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
126	$[P4/nnc\ (422)]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
126	$[P4/nnc\ (\bar{1})]$	$[P4/mmm\ (mmm)]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
127			$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
128			$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
129	$[P4/nmm\ (\bar{4}m2)]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
129	$[P4/nmm\ (2/m)]$	$[P4/mmm\ (mmm)]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
130	$[P4/ncc\ (\bar{4})]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
130	$[P4/ncc\ (\bar{1})]$	$[P4/mmm\ (mmm)]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
131	$[P4_{2}/mmc]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
132	$[P4_{2}/mcm]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
133	$[P4_{2}/nbc\ (\bar{4})]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
133	$[P4_{2}/nbc\ (\bar{1})]$	$[P4/mmm\ (mmm)]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
134	$[P4_{2}/nnm\ (\bar{4}2m)]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
134	$[P4_{2}/nnm\ (2/m)]$	$[P4/mmm\ (mmm)]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
135	$[P4_{2}/mbc]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
136	$[P4_{2}/mnm]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
137	$[P4_{2}/nmc\ (\bar{4}m2)]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
137	$[P4_{2}/nmc\ (\bar{1})]$	$[P4/mmm\ (mmm)]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
138	$[P4_{2}/ncm\ (\bar{4})]$		$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
138	$[P4_{2}/ncm\ (2/m)]$	$[P4/mmm\ (mmm)]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},0]$ ; $[0, 0,{1 \over 2}]$			$[4\cdot 1\cdot 1]$
139			$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 1]$
140			$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 1]$
141	$[I4_{1}/amd\ (\bar{4}m2)]$	$[P4_{2}/nnm\ (\bar{4}2m)]$	$[{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b}), {1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 1]$
141	$[I4_{1}/amd\ (2/m)]$	$[P4_{2}/nnm\ (2/m)]$	$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), {1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 1]$
142	$[I4_{1}/acd\ (\bar{4})]$	$[P4_{2}/nnm\ (\bar{4}2m)]$	$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), {1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 1]$
142	$[I4_{1}/acd\ (\bar{1})]$	$[P4_{2}/nnm\ (2/m)]$	$[{1 \over 2}({\bf a} - {\bf b}), {1 \over 2}({\bf a} + {\bf b}), {1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 1]$
143	P 3	$[P^{1}6/mmm]$	$[{2 \over 3}{\bf a} + {1 \over 3}{\bf b}, -{1 \over 3}{\bf a} + {1 \over 3}{\bf b}, \varepsilon {\bf c}]$	$[{2 \over 3},{1 \over 3},0]$ ;	0, 0, 0	;	$[(3\cdot \infty)\cdot 2\cdot 4]$
144	$[P3_{1}]$	$[P^{1}622]$	$[{2 \over 3}{\bf a} + {1 \over 3}{\bf b}, -{1 \over 3}{\bf a} + {1 \over 3}{\bf b}, \varepsilon {\bf c}]$	$[{2 \over 3},{1 \over 3},0]$ ;	/	;	$[(3\cdot \infty)\cdot 4]$
145	$[P3_{2}]$	$[P^{1}622]$	$[{2 \over 3}{\bf a} + {1 \over 3}{\bf b}, -{1 \over 3}{\bf a} + {1 \over 3}{\bf b}, \varepsilon {\bf c}]$	$[{2 \over 3},{1 \over 3},0]$ ;	/	;	$[(3\cdot \infty)\cdot 4]$
146	R 3 (hexag.)	$[P^{1}\bar{3}1m]$	$[{2 \over 3}{\bf a} + {1 \over 3}{\bf b}, -{1 \over 3}{\bf a} + {1 \over 3}{\bf b}, \varepsilon {\bf c}]$	0, 0, t	0, 0, 0		$[\infty \cdot 2\cdot 2]$
146	R 3 (rhomboh.)	$[P^{1}\bar{3}1m]$	$[{2 \over 3}{\bf a} - {1 \over 3}{\bf b} - {1 \over 3}{\bf c}]$ , $[-{1 \over 3}{\bf a} + {2 \over 3}{\bf b} - {1 \over 3}{\bf c}, \varepsilon ({\bf a} + {\bf b} + {\bf c})]$	r , r, r	0, 0, 0	y , x, z	$[\infty \cdot 2\cdot 2]$
147	$[P\bar{3}]$		$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$		;	$[2\cdot 1\cdot 4]$
148	$[R\bar{3}]$ (hexag.)	$[R\bar{3}m]$ (hexag.)	$[-{\bf a}, {-{\bf b}}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 2]$
148	$[R\bar{3}]$ (rhomboh.)	$[R\bar{3}m]$ (rhomboh.)	$[{1 \over 2}(-{\bf a} + {\bf b} + {\bf c})]$ , $[{1 \over 2}({\bf a} - {\bf b} + {\bf c})]$ , $[{1 \over 2}({\bf a} + {\bf b} - {\bf c})]$	$[{1 \over 2},{1 \over 2},{1 \over 2}]$		y , x, z	$[2\cdot 1\cdot 2]$
149	P 312		$[{2 \over 3}{\bf a} + {1 \over 3}{\bf b}, -{1 \over 3}{\bf a} + {1 \over 3}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{2 \over 3},{1 \over 3},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0		$[6\cdot 2\cdot 2]$
150	P 321		$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	0, 0, 0		$[2\cdot 2\cdot 2]$
151	$[P3_{1}12]$	$[P6_{2}22]$	$[{2 \over 3}{\bf a} + {1 \over 3}{\bf b}, -{1 \over 3}{\bf a} + {1 \over 3}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{2 \over 3},{1 \over 3},0]$ ; $[0, 0,{1 \over 2}]$	/		$[6\cdot 2]$
152	$[P3_{1}21]$	$[P6_{2}22]$	$[{\bf a} + {\bf b}, {-{\bf a}}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	/		$[2\cdot 2]$
153	$[P3_{2}12]$	$[P6_{4}22]$	$[{2 \over 3}{\bf a} + {1 \over 3}{\bf b}, -{1 \over 3}{\bf a} + {1 \over 3}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{2 \over 3},{1 \over 3},0]$ ; $[0, 0,{1 \over 2}]$	/		$[6\cdot 2]$
154	$[P3_{2}21]$	$[P6_{4}22]$	$[{\bf a} + {\bf b}, -{\bf a}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	/		$[2\cdot 2]$
155	R 32 (hexag.)	$[R\bar{3}m]$ (hexag.)	$[-{\bf a}, {-{\bf b}}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	0, 0, 0		$[2\cdot 2\cdot 1]$
155	R 32 (rhomboh.)	$[R\bar{3}m]$ (rhomboh.)	$[{1 \over 2}(-{\bf a} + {\bf b} + {\bf c})]$ , $[{1 \over 2}({\bf a} - {\bf b} + {\bf c})]$ , $[{1 \over 2}({\bf a} + {\bf b} - {\bf c})]$	$[{1 \over 2},{1 \over 2},{1 \over 2}]$	0, 0, 0		$[2\cdot 2\cdot 1]$
156	P 3m1	$[P^{1}6/mmm]$	$[{2 \over 3}{\bf a} + {1 \over 3}{\bf b}, -{1 \over 3}{\bf a} + {1 \over 3}{\bf b}, \varepsilon {\bf c}]$	$[{2 \over 3},{1 \over 3},0]$ ;	0, 0, 0		$[(3\cdot \infty)\cdot 2\cdot 2]$
157	P 31m	$[P^{1}6/mmm]$	$[{\bf a}]$ , $[{\bf b}]$ , $[\varepsilon {\bf c}]$	0, 0, t	0, 0, 0		$[\infty \cdot 2\cdot 2]$
158	P 3c1	$[P^{1}6/mmm]$	$[{2 \over 3}{\bf a} + {1 \over 3}{\bf b}, -{1 \over 3}{\bf a} + {1 \over 3}{\bf b}, \varepsilon {\bf c}]$	$[{2 \over 3},{1 \over 3},0]$ ;	0, 0, 0		$[(3\cdot \infty)\cdot 2\cdot 2]$
159	P 31c	$[P^{1}6/mmm]$	$[{\bf a}]$ , $[{\bf b}, \varepsilon {\bf c}]$	0, 0, t	0, 0, 0		$[\infty \cdot 2\cdot 2]$
160	R 3m (hexag.)	$[P^{1}\bar{3}1m]$	$[{2 \over 3}{\bf a} + {1 \over 3}{\bf b}, -{1 \over 3}{\bf a} + {1 \over 3}{\bf b}, \varepsilon {\bf c}]$	0, 0, t	0, 0, 0		$[\infty \cdot 2\cdot 1]$
160	R 3m (rhomboh.)	$[P^{1}\bar{3}1m]$	$[{2 \over 3}{\bf a} - {1 \over 3}{\bf b} - {1 \over 3}{\bf c}]$ , $[-{1 \over 3}{\bf a} + {2 \over 3}{\bf b} - {1 \over 3}{\bf c}]$ , $[\varepsilon ({\bf a} + {\bf b} + {\bf c})]$	r , r, r	0, 0, 0		$[\infty \cdot 2\cdot 1]$
161	R 3c (hexag.)	$[P^{1}\bar{3}1m]$	$[{2 \over 3}{\bf a} + {1 \over 3}{\bf b}, -{1 \over 3}{\bf a} + {1 \over 3}{\bf b}, \varepsilon {\bf c}]$	0, 0, t	0, 0, 0		$[\infty \cdot 2\cdot 1]$
161	R 3c (rhomboh.)	$[P^{1}\bar{3}1m]$	$[{2 \over 3}{\bf a} - {1 \over 3}{\bf b} - {1 \over 3}{\bf c}]$ , $[-{1 \over 3}{\bf a} + {2 \over 3}{\bf b} - {1 \over 3}{\bf c}]$ , $[\varepsilon ({\bf a} + {\bf b} + {\bf c})]$	r , r, r	0, 0, 0		$[\infty \cdot 2\cdot 1]$
162	$[P\bar{3}1m]$		$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 2]$
163	$[P\bar{3}1c]$		$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 2]$
164	$[P\bar{3}m1]$		$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 2]$
165	$[P\bar{3}c1]$		$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 2]$
166	$[R\bar{3}m]$ (hexag.)	$[R\bar{3}m]$ (hexag.)	$[-{\bf a}, {-{\bf b}}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 1]$
166	$[R\bar{3}m]$ (rhomboh.)	$[R\bar{3}m]$ (rhomboh.)	$[{1 \over 2}(-{\bf a} + {\bf b} + {\bf c})]$ , $[{1 \over 2}({\bf a} - {\bf b} + {\bf c})]$ , $[{1 \over 2}({\bf a} + {\bf b} - {\bf c})]$	$[{1 \over 2},{1 \over 2},{1 \over 2}]$			$[2\cdot 1\cdot 1]$
167	$[R\bar{3}c]$ (hexag.)	$[R\bar{3}m]$ (hexag.)	$[-{\bf a}, {-{\bf b}}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 1]$
167	$[R\bar{3}c]$ (rhomboh.)	$[R\bar{3}m]$ (rhomboh.)	$[{1 \over 2}(-{\bf a} + {\bf b} + {\bf c})]$ , $[{1 \over 2}({\bf a} - {\bf b} + {\bf c})]$ , $[{1 \over 2}({\bf a} + {\bf b} - {\bf c})]$	$[{1 \over 2},{1 \over 2},{1 \over 2}]$			$[2\cdot 1\cdot 1]$
168	P 6	$[P^{1}6/mmm]$	$[{\bf a}]$ , $[{\bf b}, \varepsilon {\bf c}]$	0, 0, t	0, 0, 0	y , x, z	$[\infty \cdot 2\cdot 2]$
169	$[P6_{1}]$	$[P^{1}622]$	$[{\bf a}]$ , $[{\bf b}, \varepsilon {\bf c}]$	0, 0, t	/		$[\infty \cdot 2]$
170	$[P6_{5}]$	$[P^{1}622]$	$[{\bf a}]$ , $[{\bf b}, \varepsilon {\bf c}]$	0, 0, t	/		$[\infty \cdot 2]$
171	$[P6_{2}]$	$[P^{1}622]$	$[{\bf a}]$ , $[{\bf b}, \varepsilon {\bf c}]$	0, 0, t	/		$[\infty \cdot 2]$
172	$[P6_{4}]$	$[P^{1}622]$	$[{\bf a}]$ , $[{\bf b}, \varepsilon {\bf c}]$	0, 0, t	/		$[\infty \cdot 2]$
173	$[P6_{3}]$	$[P^{1}6/mmm]$	$[{\bf a}]$ , $[{\bf b}, \varepsilon {\bf c}]$	0, 0, t	0, 0, 0	y , x, z	$[\infty \cdot 2\cdot 2]$
174	$[P\bar{6}]$		$[{2 \over 3}{\bf a} + {1 \over 3}{\bf b}, -{1 \over 3}{\bf a} + {1 \over 3}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{2 \over 3},{1 \over 3},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0	y , x, z	$[6\cdot 2\cdot 2]$
175			$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$		y , x, z	$[2\cdot 1\cdot 2]$
176	$[P6_{3}/m]$		$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$		y , x, z	$[2\cdot 1\cdot 2]$
177	P 622		$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	0, 0, 0		$[2\cdot 2\cdot 1]$
178	$[P6_{1}22]$	$[P6_{2}22]$	$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	/		$[2\cdot 1]$
179	$[P6_{5}22]$	$[P6_{4}22]$	$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	/		$[2\cdot 1]$
180	$[P6_{2}22]$	$[P6_{4}22]$	$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	/		$[2\cdot 1]$
181	$[P6_{4}22]$	$[P6_{2}22]$	$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	/		$[2\cdot 1]$
182	$[P6_{3}22]$		$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	0, 0, 0		$[2\cdot 2\cdot 1]$
183	P 6mm	$[P^{1}6/mmm]$	$[{\bf a}]$ , $[{\bf b}, \varepsilon {\bf c}]$	0, 0, t	0, 0, 0		$[\infty \cdot 2\cdot 1]$
184	P 6cc	$[P^{1}6/mmm]$	$[{\bf a}]$ , $[{\bf b}, \varepsilon {\bf c}]$	0, 0, t	0, 0, 0		$[\infty \cdot 2\cdot 1]$
185	$[P6_{3}cm]$	$[P^{1}6/mmm]$	$[{\bf a}]$ , $[{\bf b}, \varepsilon {\bf c}]$	0, 0, t	0, 0, 0		$[\infty \cdot 2\cdot 1]$
186	$[P6_{3}mc]$	$[P^{1}6/mmm]$	$[{\bf a}]$ , $[{\bf b}, \varepsilon {\bf c}]$	0, 0, t	0, 0, 0		$[\infty \cdot 2\cdot 1]$
187	$[P\bar{6}m2]$		$[{2 \over 3}{\bf a} + {1 \over 3}{\bf b}, -{1 \over 3}{\bf a} + {1 \over 3}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{2 \over 3},{1 \over 3},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0		$[6\cdot 2\cdot 1]$
188	$[P\bar{6}c2]$		$[{2 \over 3}{\bf a} + {1 \over 3}{\bf b}, -{1 \over 3}{\bf a} + {1 \over 3}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{2 \over 3},{1 \over 3},0]$ ; $[0, 0,{1 \over 2}]$	0, 0, 0		$[6\cdot 2\cdot 1]$
189	$[P\bar{6}2m]$		$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	0, 0, 0		$[2\cdot 2\cdot 1]$
190	$[P\bar{6}2c]$		$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$	0, 0, 0		$[2\cdot 2\cdot 1]$
191			$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 1]$
192			$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 1]$
193	$[P6_{3}/mcm]$		$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 1]$
194	$[P6_{3}/mmc]$		$[{\bf a}]$ , $[{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[0, 0,{1 \over 2}]$			$[2\cdot 1\cdot 1]$
195	P 23	$[Im\bar{3}m]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$	0, 0, 0	y , x, z	$[2\cdot 2\cdot 2]$
196	F 23	$[Im\bar{3}m]$	$[{1 \over 2}{\bf a}]$ , $[{1 \over 2}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{1 \over 4},{1 \over 4},{1 \over 4}]$	0, 0, 0	y , x, z	$[4\cdot 2\cdot 2]$
197	I 23	$[Im\bar{3}m]$	a , b, c		0, 0, 0	y , x, z	$[1\cdot 2\cdot 2]$
198	$[P2_{1}3]$	$[Ia\bar{3}d]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$	0, 0, 0	$[y + {1 \over 4}]$ , $[x + {1 \over 4}]$ , $[z + {1 \over 4}]$	$[2\cdot 2\cdot 2]$
199	$[I2_{1}3]$	$[Ia\bar{3}d]$	a , b, c		0, 0, 0	$[y + {1 \over 4}]$ , $[x + {1 \over 4}]$ , $[z + {1 \over 4}]$	$[1\cdot 2\cdot 2]$
200	$[Pm\bar{3}]$	$[Im\bar{3}m]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$		y , x, z	$[2\cdot 1\cdot 2]$
201	$[Pn\bar{3}\ (23)]$	$[Im\bar{3}m]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$		y , x, z	$[2\cdot 1\cdot 2]$
201	$[Pn\bar{3}\ (\bar{3})]$	$[Im\bar{3}m\ (\bar{3}m)]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$		y , x, z	$[2\cdot 1\cdot 2]$
202	$[Fm\bar{3}]$	$[Pm\bar{3}m]$	$[{1 \over 2}{\bf a}]$ , $[{1 \over 2}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},{1 \over 2}]$		y , x, z	$[2\cdot 1\cdot 2]$
203	$[Fd\bar{3}\ (23)]$	$[Pn\bar{3}m\ (\bar{4}3m)]$	$[{1 \over 2}{\bf a}]$ , $[{1 \over 2}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},{1 \over 2}]$		y , x, z	$[2\cdot 1\cdot 2]$
203	$[Fd\bar{3}\ (\bar{3})]$	$[Pn\bar{3}m\ (\bar{3}m)]$	$[{1 \over 2}{\bf a}]$ , $[{1 \over 2}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},{1 \over 2}]$		y , x, z	$[2\cdot 1\cdot 2]$
204	$[Im\bar{3}]$	$[Im\bar{3}m]$	a , b, c			y , x, z	$[1\cdot 1\cdot 2]$
205	$[Pa\bar{3}]$	$[Ia\bar{3}]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$			$[2\cdot 1\cdot 1]$
206	$[Ia\bar{3}]$	$[Ia\bar{3}d]$	a , b, c			$[y + {1 \over 4}]$ , $[x + {1 \over 4}]$ , $[z + {1 \over 4}]$	$[1\cdot 1\cdot 2]$
207	P 432	$[Im\bar{3}m]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$	0, 0, 0		$[2\cdot 2\cdot 1]$
208	$[P4_{2}32]$	$[Im\bar{3}m]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$	0, 0, 0		$[2\cdot 2\cdot 1]$
209	F 432	$[Pm\bar{3}m]$	$[{1 \over 2}{\bf a}]$ , $[{1 \over 2}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},{1 \over 2}]$	0, 0, 0		$[2\cdot 2\cdot 1]$
210	$[F4_{1}32]$	$[Pn\bar{3}m\ (\bar{4}3m)]$	$[{1 \over 2}{\bf a}]$ , $[{1 \over 2}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},{1 \over 2}]$	$[{1 \over 8},{1 \over 8},{1 \over 8}]$		$[2\cdot 2\cdot 1]$
211	I 432	$[Im\bar{3}m]$	a , b, c		0, 0, 0		$[1\cdot 2\cdot 1]$
212	$[P4_{3}32]$	$[I4_{1}32]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$	/		$[2\cdot 1]$
213	$[P4_{1}32]$	$[I4_{1}32]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$	/		$[2\cdot 1]$
214	$[I4_{1}32]$	$[Ia\bar{3}d]$	a , b, c		0, 0, 0		$[1\cdot 2\cdot 1]$
215	$[P\bar{4}3m]$	$[Im\bar{3}m]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$	0, 0, 0		$[2\cdot 2\cdot 1]$
216	$[F\bar{4}3m]$	$[Im\bar{3}m]$	$[{1 \over 2}{\bf a}]$ , $[{1 \over 2}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{1 \over 4},{1 \over 4},{1 \over 4}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
217	$[I\bar{4}3m]$	$[Im\bar{3}m]$	a , b, c		0, 0, 0		$[1\cdot 2\cdot 1]$
218	$[P\bar{4}3n]$	$[Im\bar{3}m]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$	0, 0, 0		$[2\cdot 2\cdot 1]$
219	$[F\bar{4}3c]$	$[Im\bar{3}m]$	$[{1 \over 2}{\bf a}]$ , $[{1 \over 2}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{1 \over 4},{1 \over 4},{1 \over 4}]$	0, 0, 0		$[4\cdot 2\cdot 1]$
220	$[I\bar{4}3d]$	$[Ia\bar{3}d]$	a , b, c		0, 0, 0		$[1\cdot 2\cdot 1]$
221	$[Pm\bar{3}m]$	$[Im\bar{3}m]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$			$[2\cdot 1\cdot 1]$
222	$[Pn\bar{3}n\ (432)]$	$[Im\bar{3}m]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$			$[2\cdot 1\cdot 1]$
222	$[Pn\bar{3}n\ (\bar{3})]$	$[Im\bar{3}m\ (\bar{3}m)]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$			$[2\cdot 1\cdot 1]$
223	$[Pm\bar{3}n]$	$[Im\bar{3}m]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$			$[2\cdot 1\cdot 1]$
224	$[Pn\bar{3}m\ (\bar{4}3m)]$	$[Im\bar{3}m]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$			$[2\cdot 1\cdot 1]$
224	$[Pn\bar{3}m\ (\bar{3}m)]$	$[Im\bar{3}m\ (\bar{3}m)]$	a , b, c	$[{1 \over 2},{1 \over 2},{1 \over 2}]$			$[2\cdot 1\cdot 1]$
225	$[Fm\bar{3}m]$	$[Pm\bar{3}m]$	$[{1 \over 2}{\bf a}]$ , $[{1 \over 2}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},{1 \over 2}]$			$[2\cdot 1\cdot 1]$
226	$[Fm\bar{3}c]$	$[Pm\bar{3}m]$	$[{1 \over 2}{\bf a}]$ , $[{1 \over 2}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},{1 \over 2}]$			$[2\cdot 1\cdot 1]$
227	$[Fd\bar{3}m\ (\bar{4}3m)]$	$[Pn\bar{3}m\ (\bar{4}3m)]$	$[{1 \over 2}{\bf a}]$ , $[{1 \over 2}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},{1 \over 2}]$			$[2\cdot 1\cdot 1]$
227	$[Fd\bar{3}m\ (\bar{3}m)]$	$[Pn\bar{3}m\ (\bar{3}m)]$	$[{1 \over 2}{\bf a}]$ , $[{1 \over 2}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},{1 \over 2}]$			$[2\cdot 1\cdot 1]$
228	$[Fd\bar{3}c\ (23)]$	$[Pn\bar{3}m\ (\bar{4}3m)]$	$[{1 \over 2}{\bf a}]$ , $[{1 \over 2}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},{1 \over 2}]$			$[2\cdot 1\cdot 1]$
228	$[Fd\bar{3}c\ (\bar{3})]$	$[Pn\bar{3}m\ (\bar{3}m)]$	$[{1 \over 2}{\bf a}]$ , $[{1 \over 2}{\bf b}]$ , $[{1 \over 2}{\bf c}]$	$[{1 \over 2},{1 \over 2},{1 \over 2}]$			$[2\cdot 1\cdot 1]$
229	$[Im\bar{3}m]$	$[Im\bar{3}m]$	a , b, c				$[1\cdot 1\cdot 1]$
230	$[Ia\bar{3}d]$	$[Ia\bar{3}d]$	a , b, c				$[1\cdot 1\cdot 1]$