Bilbao Crystallographic Server arrow Wyckoff Sets: Equivalent Sets of Wyckoff Positions

Wyckoff Sets of Space Group I222 (No. 23)

NOTE: The program uses the default choice for the group settings.

Letter Mult SS Rep. Equivalent WP under
Euclidean normalizer		 Equivalent WP under
affine normalizer
k 8 1 (x, y, z) k k
j 4 ..2 (0, 1/2 , z) ij efghij
i 4 ..2 (0, 0, z) ij efghij
h 4 .2. (1/2 , y, 0) gh efghij
g 4 .2. (0, y, 0) gh efghij
f 4 2.. (x, 0, 1/2 ) ef efghij
e 4 2.. (x, 0, 0) ef efghij
d 2 222 (0, 1/2 , 0) abcd abcd
c 2 222 (0, 0, 1/2 ) abcd abcd
b 2 222 (1/2 , 0, 0) abcd abcd
a 2 222 (0, 0, 0) abcd abcd

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of I222 (023) under the coset representatives of its affine normalizer


Index: 48

No. # Coset Representative Transformed WP
1x,y,z
(
   1   0   0    0
   0   1   0    0
   0   0   1    0
)
 
a b c d e f g h i j k
2x+1/2,y,z
(
   1   0   0   1/2
   0   1   0    0
   0   0   1    0
)
 
b a d c e f h g j i k
3x,y+1/2,z
(
   1   0   0    0
   0   1   0   1/2
   0   0   1    0
)
 
d c b a f e g h j i k
4x+1/2,y+1/2,z
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)
 
c d a b f e h g i j k
5-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
 
a b c d e f g h i j k
6-x+1/2,-y,-z
(
  -1   0   0   1/2
   0  -1   0    0
   0   0  -1    0
)
 
b a d c e f h g j i k
7-x,-y+1/2,-z
(
  -1   0   0    0
   0  -1   0   1/2
   0   0  -1    0
)
 
d c b a f e g h j i k
8-x+1/2,-y+1/2,-z
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1    0
)
 
c d a b f e h g i j k
9z,x,y
(
   0   0   1    0
   1   0   0    0
   0   1   0    0
)
 
a c d b i j e f g h k
10z+1/2,x,y
(
   0   0   1   1/2
   1   0   0    0
   0   1   0    0
)
 
c a b d i j f e h g k
11z,x+1/2,y
(
   0   0   1    0
   1   0   0   1/2
   0   1   0    0
)
 
b d c a j i e f h g k
12z+1/2,x+1/2,y
(
   0   0   1   1/2
   1   0   0   1/2
   0   1   0    0
)
 
d b a c j i f e g h k
13-z,-x,-y
(
   0   0  -1    0
  -1   0   0    0
   0  -1   0    0
)
 
a c d b i j e f g h k
14-z+1/2,-x,-y
(
   0   0  -1   1/2
  -1   0   0    0
   0  -1   0    0
)
 
c a b d i j f e h g k
15-z,-x+1/2,-y
(
   0   0  -1    0
  -1   0   0   1/2
   0  -1   0    0
)
 
b d c a j i e f h g k
16-z+1/2,-x+1/2,-y
(
   0   0  -1   1/2
  -1   0   0   1/2
   0  -1   0    0
)
 
d b a c j i f e g h k
17y,z,x
(
   0   1   0    0
   0   0   1    0
   1   0   0    0
)
 
a d b c g h i j e f k
18y+1/2,z,x
(
   0   1   0   1/2
   0   0   1    0
   1   0   0    0
)
 
d a c b g h j i f e k
19y,z+1/2,x
(
   0   1   0    0
   0   0   1   1/2
   1   0   0    0
)
 
c b d a h g i j f e k
20y+1/2,z+1/2,x
(
   0   1   0   1/2
   0   0   1   1/2
   1   0   0    0
)
 
b c a d h g j i e f k
21-y,-z,-x
(
   0  -1   0    0
   0   0  -1    0
  -1   0   0    0
)
 
a d b c g h i j e f k
22-y+1/2,-z,-x
(
   0  -1   0   1/2
   0   0  -1    0
  -1   0   0    0
)
 
d a c b g h j i f e k
23-y,-z+1/2,-x
(
   0  -1   0    0
   0   0  -1   1/2
  -1   0   0    0
)
 
c b d a h g i j f e k
24-y+1/2,-z+1/2,-x
(
   0  -1   0   1/2
   0   0  -1   1/2
  -1   0   0    0
)
 
b c a d h g j i e f k
25y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
 
a d c b g h e f i j k
26y+1/2,x,z
(
   0   1   0   1/2
   1   0   0    0
   0   0   1    0
)
 
d a b c g h f e j i k
27y,x+1/2,z
(
   0   1   0    0
   1   0   0   1/2
   0   0   1    0
)
 
b c d a h g e f j i k
28y+1/2,x+1/2,z
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1    0
)
 
c b a d h g f e i j k
29-y,-x,-z
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1    0
)
 
a d c b g h e f i j k
30-y+1/2,-x,-z
(
   0  -1   0   1/2
  -1   0   0    0
   0   0  -1    0
)
 
d a b c g h f e j i k
31-y,-x+1/2,-z
(
   0  -1   0    0
  -1   0   0   1/2
   0   0  -1    0
)
 
b c d a h g e f j i k
32-y+1/2,-x+1/2,-z
(
   0  -1   0   1/2
  -1   0   0   1/2
   0   0  -1    0
)
 
c b a d h g f e i j k
33z,y,x
(
   0   0   1    0
   0   1   0    0
   1   0   0    0
)
 
a c b d i j g h e f k
34z+1/2,y,x
(
   0   0   1   1/2
   0   1   0    0
   1   0   0    0
)
 
c a d b i j h g f e k
35z,y+1/2,x
(
   0   0   1    0
   0   1   0   1/2
   1   0   0    0
)
 
d b c a j i g h f e k
36z+1/2,y+1/2,x
(
   0   0   1   1/2
   0   1   0   1/2
   1   0   0    0
)
 
b d a c j i h g e f k
37-z,-y,-x
(
   0   0  -1    0
   0  -1   0    0
  -1   0   0    0
)
 
a c b d i j g h e f k
38-z+1/2,-y,-x
(
   0   0  -1   1/2
   0  -1   0    0
  -1   0   0    0
)
 
c a d b i j h g f e k
39-z,-y+1/2,-x
(
   0   0  -1    0
   0  -1   0   1/2
  -1   0   0    0
)
 
d b c a j i g h f e k
40-z+1/2,-y+1/2,-x
(
   0   0  -1   1/2
   0  -1   0   1/2
  -1   0   0    0
)
 
b d a c j i h g e f k
41x,z,y
(
   1   0   0    0
   0   0   1    0
   0   1   0    0
)
 
a b d c e f i j g h k
42x+1/2,z,y
(
   1   0   0   1/2
   0   0   1    0
   0   1   0    0
)
 
b a c d e f j i h g k
43x,z+1/2,y
(
   1   0   0    0
   0   0   1   1/2
   0   1   0    0
)
 
c d b a f e i j h g k
44x+1/2,z+1/2,y
(
   1   0   0   1/2
   0   0   1   1/2
   0   1   0    0
)
 
d c a b f e j i g h k
45-x,-z,-y
(
  -1   0   0    0
   0   0  -1    0
   0  -1   0    0
)
 
a b d c e f i j g h k
46-x+1/2,-z,-y
(
  -1   0   0   1/2
   0   0  -1    0
   0  -1   0    0
)
 
b a c d e f j i h g k
47-x,-z+1/2,-y
(
  -1   0   0    0
   0   0  -1   1/2
   0  -1   0    0
)
 
c d b a f e i j h g k
48-x+1/2,-z+1/2,-y
(
  -1   0   0   1/2
   0   0  -1   1/2
   0  -1   0    0
)
 
d c a b f e j i g h k


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