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

Wyckoff Sets of Space Group P-4b2 (No. 117)

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

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

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P-4b2 (117) 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+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) 
a b c d e f g h i
3x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
t (0,0,1/2) 
b a d c e f h g i
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 e f h g 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+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 
a b c d e f g h i
7-x,-y,-z+1/2
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1   1/2
)
-1 0,0,1/4 
b a d c e f h g i
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


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