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. 2014 Nov 28;70(Pt 12):3290–3298. doi: 10.1107/S1399004714024572

Table 1. List of space groups having only rotational symmetry elements (Sohncke groups) and the corresponding anti-Cheshire symmetry and limits for the optimal positioning of a molecule in the appropriate orientation.

The limits of the positioning region correspond to the asymmetric unit of the anti-Cheshire cell. x, y, z are fractional coordinates of the original cell. The symbol ‘Z’ relates to an infinitesimally small cell dimension in a particular direction. The location limits are somewhat modified from the version in Dauter (2013b ▶).

Space group No. Symbol Anti-Cheshire symmetry Molecule location limits
1 P1 Z 31 x, y, z = 1/2
3 P2 Z 12 0 x 1/4; 0 z 1/2; y = 1/2
4 P21 Z 12 0 x 1/4; 0 z 1/2; y = 1/2
5 C2 Z 12 0 x 1/4; 0 z 1/2; y = 1/2
16 P222 P222 0 x, y 1/4; 0 z 1/2
17 P2221 P222 0 x, y 1/4; 0 z 1/2
18 P21212 P222 0 x, y 1/4; 0 z 1/2
19 P212121 P222 0 x, y 1/4; 0 z 1/2
20 C2221 P222 0 x, y 1/4; 0 z 1/2
21 C222 P222 0 x, y 1/4; 0 z 1/2
22 F222 I222 0 x, y, z 1/4
23 I222 P222 0 x, y 1/4; 0 z 1/2
24 I212121 P222 0 x, y 1/4; 0 z 1/2
75 P4 Z 1422 0 x 1/4; x y 1/2 x; z = 1/2
76 P41 Z 1422 0 x 1/4; x y 1/2 x; z = 1/2
77 P42 Z 1422 0 x 1/4; x y 1/2 x; z = 1/2
78 P43 Z 1422 0 x 1/4; x y 1/2 x; z = 1/2
79 I4 Z 1422 0 x 1/4; x y 1/2 x; z = 1/2
80 I41 Z 1422 0 x 1/4; x y 1/2 x; z = 1/2
89 P422 P422 0 x 1/4; x y 1/2 x; 0 z 1/2
90 P4212 P422 0 x 1/4; x y 1/2 x; 0 z 1/2
91 P4122 P4222 0 x 1/4; x y 1/2 x; 0 z 1/2
92 P41212 P4222 0 x 1/4; x y 1/2 x; 0 z 1/2
93 P4222 P422 0 x 1/4; x y 1/2 x; 0 z 1/2
94 P42212 P422 0 x 1/4; x y 1/2 x; 0 z 1/2
95 P4322 P4222 0 x 1/4; x y 1/2 x; 0 z 1/2
96 P43212 P4222 0 x 1/4; x y 1/2 x; 0 z 1/2
97 I422 P422 0 x 1/4; 1/2 x y 1/2 + x; 0 z 1/2
98 I4122 P4222 0 x 1/4; 1/2 x y 1/2 + x; 0 z 1/2
143 P3 Z 1622 0 x 1/3; 0 y x/2; z = 1/2
144 P31 Z 1622 0 x 1/3; 0 y x/2; z = 1/2
145 P32 Z 1622 0 x 1/3; 0 y x/2; z = 1/2
146 R3 Z 1312 0 x 1/3; 0 y x; z = 1/2
149 P312 P622 0 x 1/3; 0 y x/2; 0 z 1/2
150 P321 P622 0 x 2/3; 0 y x/2; y 2x 1; 0 z 1/2
151 P3112 P6222 0 x 1/3; 0 y x/2; 0 z 1/2
152 P3121 P6222 0 x 2/3; 0 y x/2; y 2x 1; 0 z 1/2
153 P3212 P6422 0 x 1/3; 0 y x/2; 0 z 1/2
154 P3221 P6422 0 x 2/3; 0 y x/2; y 2x 1; 0 z 1/2
155 R32 R32 0 x 1/3; 0 y x/3; 0 z 1/2
168 P6 Z1622 0 x 2/3; 0 y x/2; y 2x 1; z = 1/2
169 P61 Z 1622 0 x 2/3; 0 y x/2; y 2x 1; z = 1/2
170 P65 Z 1622 0 x 2/3; 0 y x/2; y 2x 1; z = 1/2
171 P62 Z 1622 0 x 2/3; 0 y x/2; y 2x 1; z = 1/2
172 P64 Z 1622 0 x 2/3; 0 y x/2; y 2x 1; z = 1/2
173 P63 Z 1622 0 x 2/3; 0 y x/2; y 2x 1; z = 1/2
177 P622 P622 0 x 2/3; 0 y x/2; y 2x 1; 0 z 1/2
178 P6122 P6222 0 x 2/3; 0 y x/2; y 2x 1; 0 z 1/2
179 P6522 P6422 0 x 2/3; 0 y x/2; y 2x 1; 0 z 1/2
180 P6222 P6422 0 x 2/3; 0 y x/2; y 2x 1; 0 z 1/2
181 P6422 P6222 0 x 2/3; 0 y x/2; y 2x 1; 0 z 1/2
182 P6322 P622 0 x 2/3; 0 y x/2; y 2x 1; 0 z 1/2
195 P23 I432 0 x 1/4; x y, z 1/2 x
196 F23 I432 0 x 1/8; x y, z 1/4 x
197 I23 I432 0 x 1/4; x y, z 1/2 x
198 P213 I4132 3/8 x 1/8; 1/8 y 1/8; max(x, y, y x 1/8) z y + 1/4
199 I213 I4132 3/8 x 1/8; 1/8 y 1/8; max(x, y, y x 1/8) z y + 1/4
207 P432 I432 0 x 1/4; x y, z 1/2 x
208 P4232 I432 0 x 1/4; x y, z 1/2 x
209 F432 I432 0 x 1/8; x y, z 1/4 x
210 F4132 I432 0 x 1/8; x y, z 1/4 x
211 I432 I432 0 x 1/4; x y, z 1/2 x
212 P4332 I4132 3/8 x 1/8; 1/8 y 1/8; max(x, y, y x 1/8) z y + 1/4
213 P4132 I4132 3/8 x 1/8; 1/8 y 1/8; max(x, y, y x 1/8) z y + 1/4
214 I4132 I4132 3/8 x 1/8; 1/8 y 1/8; max(x, y, y x 1/8) z y + 1/4