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

Wyckoff Sets of Space Group P43 (No. 78)

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

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

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P43 (078) 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
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
3y,x,-z
(
   0   1   0    0
   1   0   0    0
   0   0  -1    0
)
2 x,x,0 
a
4y+1/2,x+1/2,-z
(
   0   1   0   1/2
   1   0   0   1/2
   0   0  -1    0
)
2 (1/2,1/2,0) x,x,0 
a




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


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