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

Wyckoff Sets of Space Group I-4c2 (No. 120)

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

Letter Mult SS Rep. Equivalent WP
i 16 1 (x, y, z) i
h 8 ..2 (x, x + 1/2 , 0) eh
g 8 2.. (0, 1/2 , z) fg
f 8 2.. (0, 0, z) fg
e 8 ..2 (x, x, 1/4 ) eh
d 4 2.2 2 (0, 1/2 , 0) ad
c 4 -4.. (0, 1/2 , 1/4 ) bc
b 4 -4.. (0, 0, 0) bc
a 4 2.2 2 (0, 0, 1/4 ) ad

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of I-4c2 (120) 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
2x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
t (0,0,1/2) 
a b c d e f g h i
3x+1/2,y,z+1/4
(
   1   0   0   1/2
   0   1   0    0
   0   0   1   1/4
)
t (1/2,0,1/4) 
d c b a h g f e i
4x+1/2,y,z+3/4
(
   1   0   0   1/2
   0   1   0    0
   0   0   1   3/4
)
t (1/2,0,3/4) 
d c b a h g f e i
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 i
6-x,-y,-z+1/2
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1   1/2
)
-1 0,0,1/4 
a b c d e f g h i
7-x+1/2,-y,-z+1/4
(
  -1   0   0   1/2
   0  -1   0    0
   0   0  -1   1/4
)
-1 1/4,0,1/8 
d c b a h g f e i
8-x+1/2,-y,-z+3/4
(
  -1   0   0   1/2
   0  -1   0    0
   0   0  -1   3/4
)
-1 1/4,0,3/8 
d c b a h g f e i


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