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

Wyckoff Sets of Space Group P4/mbm (No. 127)

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

Letter Mult SS Rep. Equivalent WP
l 16 1 (x, y, z) l
k 8 ..m (x, x + 1/2 , z) k
j 8 m.. (x, y, 1/2 ) ij
i 8 m.. (x, y, 0) ij
h 4 m.2 m (x, x + 1/2 , 1/2 ) gh
g 4 m.2 m (x, x + 1/2 , 0) gh
f 4 2.m m (0, 1/2 , z) f
e 4 4.. (0, 0, z) e
d 2 m.m m (0, 1/2 , 0) cd
c 2 m.m m (0, 1/2 , 1/2 ) cd
b 2 4/m.. (0, 0, 1/2 ) ab
a 2 4/m.. (0, 0, 0) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P4/mbm (127) 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 e f g h i j k l
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 j k l
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 j i k l
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 j i k l


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