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

Wyckoff Sets of Space Group F-43c (No. 219)

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

Letter Mult SS Rep. Equivalent WP
h 96 1 (x, y, z) h
g 48 2.. (x, 1/4 , 1/4 ) fg
f 48 2.. (x, 0, 0) fg
e 32 .3. (x, x, x) e
d 24 -4.. (1/4 , 0, 0) cd
c 24 -4.. (0, 1/4 , 1/4 ) cd
b 8 23. (1/4 , 1/4 , 1/4 ) ab
a 8 23. (0, 0, 0) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of F-43c (219) 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
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) 
b a d c 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) 
a b c d 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) 
b a d c 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 c d 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 
b a d c 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 
a b 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 
b a d c e g f h


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