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

Wyckoff Sets of Space Group F23 (No. 196)

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

Letter Mult SS Rep. Equivalent WP
h 48 1 (x, y, z) h
g 24 2.. (x, 1/4 , 1/4 ) fg
f 24 2.. (x, 0, 0) fg
e 16 .3. (x, x, x) e
d 4 23. (3/4 , 3/4 , 3/4 ) abcd
c 4 23. (1/4 , 1/4 , 1/4 ) abcd
b 4 23. (1/2 , 1/2 , 1/2 ) abcd
a 4 23. (0, 0, 0) abcd

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of F23 (196) under the coset representatives of its affine normalizer


The affine normalizer coincides with the Euclidean one.

Index: 16

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
2x+1/4,y+1/4,z+1/4
(
   1   0   0   1/4
   0   1   0   1/4
   0   0   1   1/4
)
t (1/4,1/4,1/4) 
d c a b e g f h
3x+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 f g h
4x+3/4,y+3/4,z+3/4
(
   1   0   0   3/4
   0   1   0   3/4
   0   0   1   3/4
)
t (3/4,3/4,3/4) 
c d b a e g f h
5-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a b d c e f g h
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
)
-1 1/8,1/8,1/8 
c d a b e g f h
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
)
-1 1/4,1/4,1/4 
b a c d e f g h
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
)
-1 3/8,3/8,3/8 
d c b a e g f h
9 y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
m x,x,z 
a b c d e f g h
10y+1/4,x+1/4,z+1/4
(
   0   1   0   1/4
   1   0   0   1/4
   0   0   1   1/4
)
d (1/4,1/4,1/4) x,x,z 
d c a b e g f h
11y+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 f g h
12y+3/4,x+3/4,z+3/4
(
   0   1   0   3/4
   1   0   0   3/4
   0   0   1   3/4
)
d (3/4,3/4,3/4) x,x,z 
c d b a e g f h
13-y,-x,-z
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1    0
)
2 x,-x,0 
a b d c e f g h
14-y+1/4,-x+1/4,-z+1/4
(
   0  -1   0   1/4
  -1   0   0   1/4
   0   0  -1   1/4
)
2 x,-x+1/4,1/8 
c d a b e g f h
15-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 c d e f g h
16-y+3/4,-x+3/4,-z+3/4
(
   0  -1   0   3/4
  -1   0   0   3/4
   0   0  -1   3/4
)
2 x,-x+3/4,3/8 
d c b a e g f h


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