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

Wyckoff Sets of Space Group P-4c2 (No. 116)

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

Letter Mult SS Rep. Equivalent WP
j 8 1 (x, y, z) j
i 4 2.. (0, 1/2 , z) i
h 4 2.. (1/2 , 1/2 , z) gh
g 4 2.. (0, 0, z) gh
f 4 ..2 (x, x, 3/4 ) ef
e 4 ..2 (x, x, 1/4 ) ef
d 2 -4.. (1/2 , 1/2 , 0) cd
c 2 -4.. (0, 0, 0) cd
b 2 2.2 2 (1/2 , 1/2 , 1/4 ) ab
a 2 2.2 2 (0, 0, 1/4 ) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P-4c2 (116) 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   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)
t (1/2,1/2,0) 
b a d c e f h g i j
3x,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 f e g h i j
4x+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 f e h g i j
5-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a b c d f e g h i j
6-x+1/2,-y+1/2,-z
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1    0
)
-1 1/4,1/4,0 
b a d c f e h g i j
7-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 j
8-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 f h g i j


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