ISO-KOV

ISO-KOV

Table 3.
Space-Group Transformations

For each space group G, we give the transformations that (a) takes operations in the setting of Kovalev (KOV) into operations in the setting of Cracknell, Davies, Miller & Love (CDML) and (b) take operations in the default settings in the International Tables of Crystallograph (IT) into the operations of CDML.

GKOV to CDMLIT to CDML
1 P1x,y,zx,y,z
2 P-1x,y,zx,y,z
3 P2-x,y,-zz,x,y
4 P2_1-x,y,-zz,x,y
5 C2-x,y,-zz,x,y
6 Pm-x,y,-zz,x,y
7 Pc-x,y,-zz,x,y
8 Cm-x,y,-zz,x,y
9 Cc-x,y,-zz,x,y
10 P2/m-x,y,-zz,x,y
11 P2_1/m-x,y,1/4-zz,x,y
12 C2/m-x,y,-zz,x,y
13 P2/c1/4-x,y,-zz,x,y
14 P2_1/c1/4-x,y,1/4-zz,x,y
15 C2/c1/4-x,y,-zz,x,y
16 P222x,y,zx,y,z
17 P222_1x,y,zx,y,z
18 P2_12_12x,y,zx,y,z
19 P2_12_12x,y,zx,y,z
20 C222_1x,y,-1/4+zx,y,z
21 C222x,y,zx,y,z
22 F222x,y,zx,y,z
23 I222x,y,zx,y,z
24 I2_12_12x,y,zx,y,z
25 Pmm2x,y,zx,y,z
26 Pmc2_1-y,x,zx,y,z
27 Pcc2x,y,zx,y,z
28 Pma2-1/4+x,y,zx,y,z
29 Pca2_1-1/4+x,y,zx,y,z
30 Pnc2-y,-1/4+x,zx,y,z
31 Pmn2_1x,y,zx,y,z
32 Pba2-1/4+x,-1/4+y,zx,y,z
33 Pna2_1-1/4+x,-1/4+y,zx,y,z
34 Pnn2-1/4+x,-1/4+y,zx,y,z
35 Cmm2x,y,zx,y,z
36 Cmc2_1x,y,zx,y,z
37 Ccc2x,y,zx,y,z
38 Amm2x,y,z-z,y,x
39 Abm2x,y,z-z,y,x
40 Ama2x,y,z-z,y,x
41 Aba2x,y,z-z,y,x
42 Fmm2x,y,zx,y,z
43 Fdd21/8+x,1/8+y,zx,y,z
44 Imm2x,y,zx,y,z
45 Iba2x,y,zx,y,z
46 Ima2x,y,zx,y,z
47 Pmmmx,y,zx,y,z
48 Pnnnx,y,z-1/4+x,-1/4+y,-1/4+z
49 Pccmx,y,-1/4+zx,y,z
50 Pbanx,y,z-1/4+x,-1/4+y,z
51 Pmmaz,x,yx,y,z
52 Pnna-1/4+y,z,-1/4+xx,y,z
53 Pmna1/4+x,y,zx,y,z
54 Pccaz,x,-1/4+yx,y,z
55 Pbamx,y,zx,y,z
56 Pccn-1/4+x,-1/4+y,-1/4+zx,y,z
57 Pbcm-z,-1/4-y,-xx,y,z
58 Pnnmx,y,1/4+zx,y,z
59 Pmmnx,y,z-1/4+x,-1/4+y,z
60 Pbcny,-1/4+z,-1/4+xx,y,z
61 Pbcax,y,zx,y,z
62 Pnma1/4-y,-1/4+x,zx,y,z
63 Cmcm-y,x,zx,y,z
64 Cmca1/4-y,x,zx,y,z
65 Cmmmx,y,zx,y,z
66 Cccmx,y,-1/4+zx,y,z
67 Cmma-1/4+x,y,zx,y,z
68 Cccax,y,zx,-1/4+y,-1/4+z
69 Fmmmx,y,zx,y,z
70 Fdddx,y,z-7/8+x,-7/8+y,-7/8+z
71 Immmx,y,zx,y,z
72 Ibamx,y,1/4+zx,y,z
73 Ibcax,y,zx,y,z
74 Immax,y,-1/4+zx,y,z
75 P4x,y,zx,y,z
76 P4_1x,y,zx,y,z
77 P4_2x,y,zx,y,z
78 P4_3x,y,zx,y,z
79 I4x,y,zx,y,z
80 I4_1x,y,zx,y,z
81 P-4x,y,zx,y,z
82 I-4x,y,zx,y,z
83 P4/mx,y,zx,y,z
84 P4_2/mx,y,-1/4+zx,y,z
85 P4/nx,y,z-3/4+x,-1/4+y,z
86 P4_2/nx,y,z-3/4+x,-3/4+y,-3/4+z
87 I4/mx,y,zx,y,z
88 I4_1/ax,y,zx,-3/4+y,-7/8+z
89 P422x,y,zx,y,z
90 P42_12x,1/2+y,zx,y,z
91 P4_122x,y,-1/4+zx,y,z
92 P4_12_12x,1/2+y,-1/8+zx,y,z
93 P4_222x,y,zx,y,z
94 P4_22_12x,-1/2+y,-1/4+zx,y,z
95 P4_322x,y,-1/4+zx,y,z
96 P4_32_12x,1/2+y,1/8+zx,y,z
97 I422x,y,zx,y,z
98 I4_122x,y,zx,y,z
99 P4mmx,y,zx,y,z
100 P4bmx,y,zx,y,z
101 P4_2cmx,y,zx,y,z
102 P4_2nmx,1/2+y,zx,y,z
103 P4ccx,y,zx,y,z
104 P4ncx,y,zx,y,z
105 P4_2mcx,y,zx,y,z
106 P4_2bcx,y,zx,y,z
107 I4mmx,y,zx,y,z
108 I4cmx,y,zx,y,z
109 I4_1mdx,y,zx,y,z
110 I4_1cdx,y,zx,y,z
111 P-42mx,y,zx,y,z
112 P-42cx,y,zx,y,z
113 P-42_1mx,y,zx,y,z
114 P-42_1cx,y,zx,y,z
115 P-4m2x,y,zx,y,z
116 P-4c2x,y,zx,y,z
117 P-4b2x,y,zx,y,z
118 P-4n2x,y,zx,y,z
119 I-4m2x,y,zx,y,z
120 I-4c2x,y,zx,y,z
121 I-42mx,y,zx,y,z
122 I-42d-1/2+x,y,-1/4+zx,y,z
123 P4/mmmx,y,zx,y,z
124 P4/mccx,y,1/4+zx,y,z
125 P4/nbmx,y,z-3/4+x,-3/4+y,z
126 P4/nncx,y,z-3/4+x,-3/4+y,-3/4+z
127 P4/mbmx,y,zx,y,z
128 P4/mncx,y,-1/4+zx,y,z
129 P4/nmmx,-1/2+y,z-3/4+x,-1/4+y,z
130 P4/nccx,-1/2+y,-1/4+z-3/4+x,-1/4+y,z
131 P4_2/mmcx,y,zx,y,z
132 P4_2/mcmx,y,1/4+zx,y,z
133 P4_2/nbcx,-1/2+y,-1/4+z-3/4+x,-1/4+y,-3/4+z
134 P4_2/nnmx,-1/2+y,z-3/4+x,-1/4+y,-3/4+z
135 P4_2/mbcx,y,zx,y,z
136 P4_2/mnmx,-1/2+y,-1/4+zx,y,z
137 P4_2/nmcx,-1/2+y,-1/4+z-3/4+x,-1/4+y,-3/4+z
138 P4_2/ncmx,-1/2+y,z-3/4+x,-1/4+y,-3/4+z
139 I4/mmmx,y,zx,y,z
140 I4/mcmx,y,-1/4+zx,y,z
141 I4_1/amdx,y,zx,-1/4+y,-7/8+z
142 I4_1/acdx,y,1/4+zx,-1/4+y,-7/8+z
143 P3x,y,zx,y,z
144 P3_1x,y,zx,y,z
145 P3_2x,y,zx,y,z
146 R31/3x-2/3y,2/3x-1/3y,zy,-x+y,z
147 P-3x,y,zx,y,z
148 R-31/3x-2/3y,2/3x-1/3y,zy,-x+y,z
149 P312x,y,zx,y,z
150 P321x,y,zx,y,z
151 P3_112x,y,-1/3+zx,y,-1/6+z
152 P3_121x,y,-1/3+zx,y,z
153 P3_212x,y,-7/6+zx,y,-5/6+z
154 P3_221x,y,-1/3+zx,y,-1/6+z
155 R321/3x-2/3y,2/3x-1/3y,zy,-x+y,z
156 P3m1x,y,zx,y,z
157 P31mx,y,zx,y,z
158 P3c1x,y,zx,y,z
159 P31cx,y,zx,y,z
160 R3m1/3x-2/3y,2/3x-1/3y,zy,-x+y,z
161 R3c1/3x-2/3y,2/3x-1/3y,zy,-x+y,z
162 P-31mx,y,zx,y,z
163 P-31cx,y,-1/4+zx,y,z
164 P-3m1x,y,zx,y,z
165 P-3c1x,y,-1/4+zx,y,z
166 R-3m1/3x-2/3y,2/3x-1/3y,zy,-x+y,z
167 R-3c1/3x-2/3y,2/3x-1/3y,-1/4+zy,-x+y,z
168 P6x,y,zx,y,z
169 P6_1x,y,zx,y,z
170 P6_5x,y,zx,y,z
171 P6_2x,y,zx,y,z
172 P6_4x,y,zx,y,z
173 P6_3x,y,zx,y,z
174 P-6x,y,zx,y,z
175 P6/mx,y,zx,y,z
176 P6_3/mx,y,zx,y,z
177 P622x,y,zx,y,z
178 P6_122x,y,-1/6+zx,y,z
179 P6_522x,y,-1/3+zx,y,z
180 P6_222x,y,-1/3+zx,y,z
181 P6_422x,y,1/3+zx,y,z
182 P6_322x,y,zx,y,z
183 P6mmx,y,zx,y,z
184 P6ccx,y,zx,y,z
185 P6_3cmx,y,zx,y,z
186 P6_3mcx,y,zx,y,z
187 P-6m2x,y,zx,y,z
188 P-6c2x,y,zx,y,z
189 P-62mx,y,zx,y,z
190 P-62cx,y,zx,y,z
191 P6/mmmx,y,zx,y,z
192 P6/mccx,y,1/4+zx,y,z
193 P6_3/mcmx,y,1/4+zx,y,z
194 P6_3/mmcx,y,zx,y,z
195 P23x,y,zx,y,z
196 F23x,y,zx,y,z
197 I23x,y,zx,y,z
198 P2_13x,y,zx,y,z
199 I2_13x,y,zx,y,z
200 Pm-3x,y,zx,y,z
201 Pn-3x,y,z-3/4+x,-3/4+y,-3/4+z
202 Fm-3x,y,zx,y,z
203 Fd-3x,y,z-7/8+x,-7/8+y,-7/8+z
204 Im-3x,y,zx,y,z
205 Pa-3x,y,zx,y,z
206 Ia-3x,y,zx,y,z
207 P432x,y,zx,y,z
208 P4_232x,y,zx,y,z
209 F432x,y,zx,y,z
210 F4_132x,y,zx,y,z
211 I432x,y,zx,y,z
212 P4_332x,y,zx,y,z
213 P4_132x,y,zx,y,z
214 I4_132x,y,zx,y,z
215 P-43mx,y,zx,y,z
216 F-43mx,y,zx,y,z
217 I-43mx,y,zx,y,z
218 P-43nx,y,zx,y,z
219 F-43cx,y,zx,y,z
220 I-43dx,y,zx,y,z
221 Pm-3mx,y,zx,y,z
222 Pn-3nx,y,z-3/4+x,-3/4+y,-3/4+z
223 Pm-3nx,y,zx,y,z
224 Pn-3mx,y,z-3/4+x,-3/4+y,-3/4+z
225 Fm-3mx,y,zx,y,z
226 Fm-3c1/4+x,1/4+y,1/4+zx,y,z
227 Fd-3m-1/8+x,-1/8+y,-1/8+zx,y,z
228 Fd-3c-3/8+x,-3/8+y,-3/8+zx,y,z
229 Im-3mx,y,zx,y,z
230 Ia-3dx,y,zx,y,z