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

Wyckoff Sets of Space Group P4 (No. 75)

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

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

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P4 (075) 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
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
3y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
m x,x,z
a b c d
4y+1/2,x+1/2,z
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1    0
)
g (1/2,1/2,0) x,x,z
b a c d
5-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0
a b c d
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 c d
7-y,-x,-z
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1    0
)
2 x,-x,0
a b c d
8-y+1/2,-x+1/2,-z
(
   0  -1   0   1/2
  -1   0   0   1/2
   0   0  -1    0
)
2 x,-x+1/2,0
b a c d




Additional traslations generators


No. # Continuous TranslationsGeometrical Interpretation Transformed WP
1 x,y,z+t
(
   1   0   0    0
   0   1   0    0
   0   0   1    t
)
t (0,0,t)
a b c d


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