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

Wyckoff Sets of Space Group P21 (No. 4) [unique axis b]

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

Letter Mult SS Rep. Equivalent WP
a 2 1 (x, y, z) a

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P21 (004) [unique axis b] under the coset representatives of its Euclidean normalizer


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
2x+1/2,y,z
(
   1   0   0   1/2
   0   1   0    0
   0   0   1    0
)
t (1/2,0,0) 
a
3x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
t (0,0,1/2) 
a
4x+1/2,y,z+1/2
(
   1   0   0   1/2
   0   1   0    0
   0   0   1   1/2
)
t (1/2,0,1/2) 
a
5-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a
6-x+1/2,-y,-z
(
  -1   0   0   1/2
   0  -1   0    0
   0   0  -1    0
)
-1 1/4,0,0 
a
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
8-x+1/2,-y,-z+1/2
(
  -1   0   0   1/2
   0  -1   0    0
   0   0  -1   1/2
)
-1 1/4,0,1/4 
a




Additional traslations generators


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


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