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

Wyckoff Sets of Space Group P213 (No. 198)

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

Letter Mult SS Rep. Equivalent WP
b 12 1 (x, y, z) b
a 4 .3. (x, x, x) a

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P213 (198) 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
2x+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) 
a b
3-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a b
4-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 
a b
5y+1/4,x+1/4,z+1/4
(
   0   1   0   1/4
   1   0   0   1/4
   0   0   1   1/4
)
d (1/4,1/4,1/4) x,x,z 
a b
6y+3/4,x+3/4,z+3/4
(
   0   1   0   3/4
   1   0   0   3/4
   0   0   1   3/4
)
d (3/4,3/4,3/4) x,x,z 
a b
7-y+1/4,-x+1/4,-z+1/4
(
   0  -1   0   1/4
  -1   0   0   1/4
   0   0  -1   1/4
)
2 x,-x+1/4,1/8 
a b
8-y+3/4,-x+3/4,-z+3/4
(
   0  -1   0   3/4
  -1   0   0   3/4
   0   0  -1   3/4
)
2 x,-x+3/4,3/8 
a b


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