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

Wyckoff Sets of Space Group F222 (No. 22)

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 16 1 (x, y, z) k k
j 8 2.. (x, 1/4 , 1/4 ) efghij efghij
i 8 .2. (1/4 , y, 1/4 ) efghij efghij
h 8 ..2 (1/4 , 1/4 , z) efghij efghij
g 8 ..2 (0, 0, z) efghij efghij
f 8 .2. (0, y, 0) efghij efghij
e 8 2.. (x, 0, 0) efghij efghij
d 4 222 (1/4 , 1/4 , 3/4 ) abcd abcd
c 4 222 (1/4 , 1/4 , 1/4 ) abcd abcd
b 4 222 (0, 0, 1/2 ) abcd abcd
a 4 222 (0, 0, 0) abcd abcd

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of F222 (022) 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+1/4,y+1/4,z+1/4
(
   1   0   0   1/4
   0   1   0   1/4
   0   0   1   1/4
)
 
d c a b j i h g f e k
3x+1/2,y+1/2,z+1/2
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1   1/2
)
 
b a d c e f g h i j k
4x+3/4,y+3/4,z+3/4
(
   1   0   0   3/4
   0   1   0   3/4
   0   0   1   3/4
)
 
c d b a j i h g f e k
5-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
 
a b d c e f g h i j k
6-x+1/4,-y+1/4,-z+1/4
(
  -1   0   0   1/4
   0  -1   0   1/4
   0   0  -1   1/4
)
 
c d a b j i h g f e k
7-x+1/2,-y+1/2,-z+1/2
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1   1/2
)
 
b a c d e f g h i j k
8-x+3/4,-y+3/4,-z+3/4
(
  -1   0   0   3/4
   0  -1   0   3/4
   0   0  -1   3/4
)
 
d c b a j i h g f e k
9z,x,y
(
   0   0   1    0
   1   0   0    0
   0   1   0    0
)
 
a b c d g e f i j h k
10z+1/4,x+1/4,y+1/4
(
   0   0   1   1/4
   1   0   0   1/4
   0   1   0   1/4
)
 
d c a b h j i f e g k
11z+1/2,x+1/2,y+1/2
(
   0   0   1   1/2
   1   0   0   1/2
   0   1   0   1/2
)
 
b a d c g e f i j h k
12z+3/4,x+3/4,y+3/4
(
   0   0   1   3/4
   1   0   0   3/4
   0   1   0   3/4
)
 
c d b a h j i f e g k
13-z,-x,-y
(
   0   0  -1    0
  -1   0   0    0
   0  -1   0    0
)
 
a b d c g e f i j h k
14-z+1/4,-x+1/4,-y+1/4
(
   0   0  -1   1/4
  -1   0   0   1/4
   0  -1   0   1/4
)
 
c d a b h j i f e g k
15-z+1/2,-x+1/2,-y+1/2
(
   0   0  -1   1/2
  -1   0   0   1/2
   0  -1   0   1/2
)
 
b a c d g e f i j h k
16-z+3/4,-x+3/4,-y+3/4
(
   0   0  -1   3/4
  -1   0   0   3/4
   0  -1   0   3/4
)
 
d c b a h j i f e g k
17y,z,x
(
   0   1   0    0
   0   0   1    0
   1   0   0    0
)
 
a b c d f g e j h i k
18y+1/4,z+1/4,x+1/4
(
   0   1   0   1/4
   0   0   1   1/4
   1   0   0   1/4
)
 
d c a b i h j e g f k
19y+1/2,z+1/2,x+1/2
(
   0   1   0   1/2
   0   0   1   1/2
   1   0   0   1/2
)
 
b a d c f g e j h i k
20y+3/4,z+3/4,x+3/4
(
   0   1   0   3/4
   0   0   1   3/4
   1   0   0   3/4
)
 
c d b a i h j e g f k
21-y,-z,-x
(
   0  -1   0    0
   0   0  -1    0
  -1   0   0    0
)
 
a b d c f g e j h i k
22-y+1/4,-z+1/4,-x+1/4
(
   0  -1   0   1/4
   0   0  -1   1/4
  -1   0   0   1/4
)
 
c d a b i h j e g f k
23-y+1/2,-z+1/2,-x+1/2
(
   0  -1   0   1/2
   0   0  -1   1/2
  -1   0   0   1/2
)
 
b a c d f g e j h i k
24-y+3/4,-z+3/4,-x+3/4
(
   0  -1   0   3/4
   0   0  -1   3/4
  -1   0   0   3/4
)
 
d c b a i h j e g f k
25y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
 
a b c d f e g h j i k
26y+1/4,x+1/4,z+1/4
(
   0   1   0   1/4
   1   0   0   1/4
   0   0   1   1/4
)
 
d c a b i j h g e f k
27y+1/2,x+1/2,z+1/2
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1   1/2
)
 
b a d c f e g h j i k
28y+3/4,x+3/4,z+3/4
(
   0   1   0   3/4
   1   0   0   3/4
   0   0   1   3/4
)
 
c d b a i j h g e f k
29-y,-x,-z
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1    0
)
 
a b d c f e g h j i k
30-y+1/4,-x+1/4,-z+1/4
(
   0  -1   0   1/4
  -1   0   0   1/4
   0   0  -1   1/4
)
 
c d a b i j h g e f k
31-y+1/2,-x+1/2,-z+1/2
(
   0  -1   0   1/2
  -1   0   0   1/2
   0   0  -1   1/2
)
 
b a c d f e g h j i k
32-y+3/4,-x+3/4,-z+3/4
(
   0  -1   0   3/4
  -1   0   0   3/4
   0   0  -1   3/4
)
 
d c b a i j h g e f k
33z,y,x
(
   0   0   1    0
   0   1   0    0
   1   0   0    0
)
 
a b c d g f e j i h k
34z+1/4,y+1/4,x+1/4
(
   0   0   1   1/4
   0   1   0   1/4
   1   0   0   1/4
)
 
d c a b h i j e f g k
35z+1/2,y+1/2,x+1/2
(
   0   0   1   1/2
   0   1   0   1/2
   1   0   0   1/2
)
 
b a d c g f e j i h k
36z+3/4,y+3/4,x+3/4
(
   0   0   1   3/4
   0   1   0   3/4
   1   0   0   3/4
)
 
c d b a h i j e f g k
37-z,-y,-x
(
   0   0  -1    0
   0  -1   0    0
  -1   0   0    0
)
 
a b d c g f e j i h k
38-z+1/4,-y+1/4,-x+1/4
(
   0   0  -1   1/4
   0  -1   0   1/4
  -1   0   0   1/4
)
 
c d a b h i j e f g k
39-z+1/2,-y+1/2,-x+1/2
(
   0   0  -1   1/2
   0  -1   0   1/2
  -1   0   0   1/2
)
 
b a c d g f e j i h k
40-z+3/4,-y+3/4,-x+3/4
(
   0   0  -1   3/4
   0  -1   0   3/4
  -1   0   0   3/4
)
 
d c b a h i j e f g k
41x,z,y
(
   1   0   0    0
   0   0   1    0
   0   1   0    0
)
 
a b c d e g f i h j k
42x+1/4,z+1/4,y+1/4
(
   1   0   0   1/4
   0   0   1   1/4
   0   1   0   1/4
)
 
d c a b j h i f g e k
43x+1/2,z+1/2,y+1/2
(
   1   0   0   1/2
   0   0   1   1/2
   0   1   0   1/2
)
 
b a d c e g f i h j k
44x+3/4,z+3/4,y+3/4
(
   1   0   0   3/4
   0   0   1   3/4
   0   1   0   3/4
)
 
c d b a j h i f g e k
45-x,-z,-y
(
  -1   0   0    0
   0   0  -1    0
   0  -1   0    0
)
 
a b d c e g f i h j k
46-x+1/4,-z+1/4,-y+1/4
(
  -1   0   0   1/4
   0   0  -1   1/4
   0  -1   0   1/4
)
 
c d a b j h i f g e k
47-x+1/2,-z+1/2,-y+1/2
(
  -1   0   0   1/2
   0   0  -1   1/2
   0  -1   0   1/2
)
 
b a c d e g f i h j k
48-x+3/4,-z+3/4,-y+3/4
(
  -1   0   0   3/4
   0   0  -1   3/4
   0  -1   0   3/4
)
 
d c b a j h i f g e k


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