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

Wyckoff Sets of Space Group I212121 (No. 24)

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
d 8 1 (x, y, z) d d
c 4 ..2 (0, 1/4 , z) c abc
b 4 .2. (1/4 , y, 0) b abc
a 4 2.. (x, 0, 1/4 ) a abc

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Transformation of the Wyckoff Positions of I212121 (024) 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
2x+1/2,y,z
(
   1   0   0   1/2
   0   1   0    0
   0   0   1    0
)
 
a b c d
3x,y+1/2,z
(
   1   0   0    0
   0   1   0   1/2
   0   0   1    0
)
 
a b c d
4x+1/2,y+1/2,z
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)
 
a b c d
5-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
 
a b c d
6-x+1/2,-y,-z
(
  -1   0   0   1/2
   0  -1   0    0
   0   0  -1    0
)
 
a b c d
7-x,-y+1/2,-z
(
  -1   0   0    0
   0  -1   0   1/2
   0   0  -1    0
)
 
a b c d
8-x+1/2,-y+1/2,-z
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1    0
)
 
a b c d
9z,x,y
(
   0   0   1    0
   1   0   0    0
   0   1   0    0
)
 
c a b d
10z+1/2,x,y
(
   0   0   1   1/2
   1   0   0    0
   0   1   0    0
)
 
c a b d
11z,x+1/2,y
(
   0   0   1    0
   1   0   0   1/2
   0   1   0    0
)
 
c a b d
12z+1/2,x+1/2,y
(
   0   0   1   1/2
   1   0   0   1/2
   0   1   0    0
)
 
c a b d
13-z,-x,-y
(
   0   0  -1    0
  -1   0   0    0
   0  -1   0    0
)
 
c a b d
14-z+1/2,-x,-y
(
   0   0  -1   1/2
  -1   0   0    0
   0  -1   0    0
)
 
c a b d
15-z,-x+1/2,-y
(
   0   0  -1    0
  -1   0   0   1/2
   0  -1   0    0
)
 
c a b d
16-z+1/2,-x+1/2,-y
(
   0   0  -1   1/2
  -1   0   0   1/2
   0  -1   0    0
)
 
c a b d
17y,z,x
(
   0   1   0    0
   0   0   1    0
   1   0   0    0
)
 
b c a d
18y+1/2,z,x
(
   0   1   0   1/2
   0   0   1    0
   1   0   0    0
)
 
b c a d
19y,z+1/2,x
(
   0   1   0    0
   0   0   1   1/2
   1   0   0    0
)
 
b c a d
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
21-y,-z,-x
(
   0  -1   0    0
   0   0  -1    0
  -1   0   0    0
)
 
b c a d
22-y+1/2,-z,-x
(
   0  -1   0   1/2
   0   0  -1    0
  -1   0   0    0
)
 
b c a d
23-y,-z+1/2,-x
(
   0  -1   0    0
   0   0  -1   1/2
  -1   0   0    0
)
 
b c a d
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
25y+1/4,x+1/4,z+1/4
(
   0   1   0   1/4
   1   0   0   1/4
   0   0   1   1/4
)
 
b a c d
26y+3/4,x+1/4,z+1/4
(
   0   1   0   3/4
   1   0   0   1/4
   0   0   1   1/4
)
 
b a c d
27y+1/4,x+3/4,z+1/4
(
   0   1   0   1/4
   1   0   0   3/4
   0   0   1   1/4
)
 
b a c d
28y+3/4,x+3/4,z+1/4
(
   0   1   0   3/4
   1   0   0   3/4
   0   0   1   1/4
)
 
b a c d
29-y+1/4,-x+1/4,-z+1/4
(
   0  -1   0   1/4
  -1   0   0   1/4
   0   0  -1   1/4
)
 
b a c d
30-y+3/4,-x+1/4,-z+1/4
(
   0  -1   0   3/4
  -1   0   0   1/4
   0   0  -1   1/4
)
 
b a c d
31-y+1/4,-x+3/4,-z+1/4
(
   0  -1   0   1/4
  -1   0   0   3/4
   0   0  -1   1/4
)
 
b a c d
32-y+3/4,-x+3/4,-z+1/4
(
   0  -1   0   3/4
  -1   0   0   3/4
   0   0  -1   1/4
)
 
b a c d
33z+1/4,y+1/4,x+1/4
(
   0   0   1   1/4
   0   1   0   1/4
   1   0   0   1/4
)
 
c b a d
34z+3/4,y+1/4,x+1/4
(
   0   0   1   3/4
   0   1   0   1/4
   1   0   0   1/4
)
 
c b a d
35z+1/4,y+3/4,x+1/4
(
   0   0   1   1/4
   0   1   0   3/4
   1   0   0   1/4
)
 
c b a d
36z+3/4,y+3/4,x+1/4
(
   0   0   1   3/4
   0   1   0   3/4
   1   0   0   1/4
)
 
c b a d
37-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 b a d
38-z+3/4,-y+1/4,-x+1/4
(
   0   0  -1   3/4
   0  -1   0   1/4
  -1   0   0   1/4
)
 
c b a d
39-z+1/4,-y+3/4,-x+1/4
(
   0   0  -1   1/4
   0  -1   0   3/4
  -1   0   0   1/4
)
 
c b a d
40-z+3/4,-y+3/4,-x+1/4
(
   0   0  -1   3/4
   0  -1   0   3/4
  -1   0   0   1/4
)
 
c b a d
41x+1/4,z+1/4,y+1/4
(
   1   0   0   1/4
   0   0   1   1/4
   0   1   0   1/4
)
 
a c b d
42x+3/4,z+1/4,y+1/4
(
   1   0   0   3/4
   0   0   1   1/4
   0   1   0   1/4
)
 
a c b d
43x+1/4,z+3/4,y+1/4
(
   1   0   0   1/4
   0   0   1   3/4
   0   1   0   1/4
)
 
a c b d
44x+3/4,z+3/4,y+1/4
(
   1   0   0   3/4
   0   0   1   3/4
   0   1   0   1/4
)
 
a c b d
45-x+1/4,-z+1/4,-y+1/4
(
  -1   0   0   1/4
   0   0  -1   1/4
   0  -1   0   1/4
)
 
a c b d
46-x+3/4,-z+1/4,-y+1/4
(
  -1   0   0   3/4
   0   0  -1   1/4
   0  -1   0   1/4
)
 
a c b d
47-x+1/4,-z+3/4,-y+1/4
(
  -1   0   0   1/4
   0   0  -1   3/4
   0  -1   0   1/4
)
 
a c b d
48-x+3/4,-z+3/4,-y+1/4
(
  -1   0   0   3/4
   0   0  -1   3/4
   0  -1   0   1/4
)
 
a c b d


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