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

Wyckoff Sets of Space Group P21212 (No. 18)

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
c 4 1 (x, y, z) c c
b 2 ..2 (0, 1/2 , z) ab ab
a 2 ..2 (0, 0, z) ab ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P21212 (018) under the coset representatives of its affine normalizer


Index: 32

No. # Coset Representative Transformed WP
1x,y,z
(
   1   0   0    0
   0   1   0    0
   0   0   1    0
)
 
a b c
2x+1/2,y,z
(
   1   0   0   1/2
   0   1   0    0
   0   0   1    0
)
 
b a c
3x,y+1/2,z
(
   1   0   0    0
   0   1   0   1/2
   0   0   1    0
)
 
b a c
4x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
 
a b c
5x+1/2,y+1/2,z
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)
 
a b c
6x+1/2,y,z+1/2
(
   1   0   0   1/2
   0   1   0    0
   0   0   1   1/2
)
 
b a c
7x,y+1/2,z+1/2
(
   1   0   0    0
   0   1   0   1/2
   0   0   1   1/2
)
 
b a c
8x+1/2,y+1/2,z+1/2
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1   1/2
)
 
a b c
9-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
 
a b c
10-x+1/2,-y,-z
(
  -1   0   0   1/2
   0  -1   0    0
   0   0  -1    0
)
 
b a c
11-x,-y+1/2,-z
(
  -1   0   0    0
   0  -1   0   1/2
   0   0  -1    0
)
 
b a c
12-x,-y,-z+1/2
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1   1/2
)
 
a b c
13-x+1/2,-y+1/2,-z
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1    0
)
 
a b c
14-x+1/2,-y,-z+1/2
(
  -1   0   0   1/2
   0  -1   0    0
   0   0  -1   1/2
)
 
b a c
15-x,-y+1/2,-z+1/2
(
  -1   0   0    0
   0  -1   0   1/2
   0   0  -1   1/2
)
 
b a c
16-x+1/2,-y+1/2,-z+1/2
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1   1/2
)
 
a b c
17y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
 
a b c
18y+1/2,x,z
(
   0   1   0   1/2
   1   0   0    0
   0   0   1    0
)
 
b a c
19y,x+1/2,z
(
   0   1   0    0
   1   0   0   1/2
   0   0   1    0
)
 
b a c
20y,x,z+1/2
(
   0   1   0    0
   1   0   0    0
   0   0   1   1/2
)
 
a b c
21y+1/2,x+1/2,z
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1    0
)
 
a b c
22y+1/2,x,z+1/2
(
   0   1   0   1/2
   1   0   0    0
   0   0   1   1/2
)
 
b a c
23y,x+1/2,z+1/2
(
   0   1   0    0
   1   0   0   1/2
   0   0   1   1/2
)
 
b a c
24y+1/2,x+1/2,z+1/2
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1   1/2
)
 
a b c
25-y,-x,-z
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1    0
)
 
a b c
26-y+1/2,-x,-z
(
   0  -1   0   1/2
  -1   0   0    0
   0   0  -1    0
)
 
b a c
27-y,-x+1/2,-z
(
   0  -1   0    0
  -1   0   0   1/2
   0   0  -1    0
)
 
b a c
28-y,-x,-z+1/2
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1   1/2
)
 
a b c
29-y+1/2,-x+1/2,-z
(
   0  -1   0   1/2
  -1   0   0   1/2
   0   0  -1    0
)
 
a b c
30-y+1/2,-x,-z+1/2
(
   0  -1   0   1/2
  -1   0   0    0
   0   0  -1   1/2
)
 
b a c
31-y,-x+1/2,-z+1/2
(
   0  -1   0    0
  -1   0   0   1/2
   0   0  -1   1/2
)
 
b a c
32-y+1/2,-x+1/2,-z+1/2
(
   0  -1   0   1/2
  -1   0   0   1/2
   0   0  -1   1/2
)
 
a b c


Bilbao Crystallographic Server
http://www.cryst.ehu.es 		For comments, please mail to
administrador.bcs@ehu.eus