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

Wyckoff Sets of Space Group C222 (No. 21)

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
l 8 1 (x, y, z) l l
k 4 ..2 (1/4 , 1/4 , z) k k
j 4 ..2 (0, 1/2 , z) ij ij
i 4 ..2 (0, 0, z) ij ij
h 4 .2. (0, y, 1/2 ) gh efgh
g 4 .2. (0, y, 0) gh efgh
f 4 2.. (x, 0, 1/2 ) ef efgh
e 4 2.. (x, 0, 0) ef efgh
d 2 222 (0, 0, 1/2 ) abcd abcd
c 2 222 (1/2 , 0, 1/2 ) abcd abcd
b 2 222 (0, 1/2 , 0) abcd abcd
a 2 222 (0, 0, 0) abcd abcd

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of C222 (021) under the coset representatives of its affine normalizer


Index: 16

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 l
2x+1/2,y,z
(
   1   0   0   1/2
   0   1   0    0
   0   0   1    0
)
 
b a d c e f g h j i k l
3x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
 
d c b a f e h g i j k l
4x+1/2,y,z+1/2
(
   1   0   0   1/2
   0   1   0    0
   0   0   1   1/2
)
 
c d a b f e h g j i k l
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 l
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 g h j i k l
7-x,-y,-z+1/2
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1   1/2
)
 
d c b a f e h g i j k l
8-x+1/2,-y,-z+1/2
(
  -1   0   0   1/2
   0  -1   0    0
   0   0  -1   1/2
)
 
c d a b f e h g j i k l
9y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
 
a b c d g h e f i j k l
10y+1/2,x,z
(
   0   1   0   1/2
   1   0   0    0
   0   0   1    0
)
 
b a d c g h e f j i k l
11y,x,z+1/2
(
   0   1   0    0
   1   0   0    0
   0   0   1   1/2
)
 
d c b a h g f e i j k l
12y+1/2,x,z+1/2
(
   0   1   0   1/2
   1   0   0    0
   0   0   1   1/2
)
 
c d a b h g f e j i k l
13-y,-x,-z
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1    0
)
 
a b c d g h e f i j k l
14-y+1/2,-x,-z
(
   0  -1   0   1/2
  -1   0   0    0
   0   0  -1    0
)
 
b a d c g h e f j i k l
15-y,-x,-z+1/2
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1   1/2
)
 
d c b a h g f e i j k l
16-y+1/2,-x,-z+1/2
(
   0  -1   0   1/2
  -1   0   0    0
   0   0  -1   1/2
)
 
c d a b h g f e j i k l


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