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

Wyckoff Sets of Space Group P42bc (No. 106)

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

Letter Mult SS Rep. Equivalent WP
c 8 1 (x, y, z) c
b 4 2.. (0, 1/2 , z) b
a 4 2.. (0, 0, z) a

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P42bc (106) 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
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
3-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a b c
4-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 
a b c




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


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