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

Wyckoff Sets of Space Group P4122 (No. 91)

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

Letter Mult SS Rep. Equivalent WP
d 8 1 (x, y, z) d
c 4 ..2 (x, x, 3/8 ) c
b 4 .2. (1/2 , y, 0) ab
a 4 .2. (0, y, 0) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P4122 (091) under the coset representatives of its affine normalizer


The affine normalizer coincides with the Euclidean one.

Index: 4

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
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 c d
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
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 c d


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