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

Wyckoff Sets of Space Group P23 (No. 195)

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

Letter Mult SS Rep. Equivalent WP
j 12 1 (x, y, z) j
i 6 2.. (x, 1/2 , 1/2 ) fi
h 6 2.. (x, 1/2 , 0) gh
g 6 2.. (x, 0, 1/2 ) gh
f 6 2.. (x, 0, 0) fi
e 4 .3. (x, x, x) e
d 3 222 . . (1/2 , 0, 0) cd
c 3 222 . . (0, 1/2 , 1/2 ) cd
b 1 23. (1/2 , 1/2 , 1/2 ) ab
a 1 23. (0, 0, 0) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P23 (195) under the coset representatives of its affine normalizer


The affine normalizer coincides with the Euclidean one.

Index: 8

No. # Coset RepresentativeGeometrical Interpretation Transformed WP
1x,y,z
(
   1   0   0    0
   0   1   0    0
   0   0   1    0
)
1 
a b c d e f g h i j
2x+1/2,y+1/2,z+1/2
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1   1/2
)
t (1/2,1/2,1/2) 
b a d c e i h g f j
3-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a b c d e f g h i j
4-x+1/2,-y+1/2,-z+1/2
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1   1/2
)
-1 1/4,1/4,1/4 
b a d c e i h g f j
5y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
m x,x,z 
a b c d e f h g i j
6y+1/2,x+1/2,z+1/2
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1   1/2
)
n (1/2,1/2,1/2) x,x,z 
b a d c e i g h f j
7-y,-x,-z
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1    0
)
2 x,-x,0 
a b c d e f h g i j
8-y+1/2,-x+1/2,-z+1/2
(
   0  -1   0   1/2
  -1   0   0   1/2
   0   0  -1   1/2
)
2 x,-x+1/2,1/4 
b a d c e i g h f j


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