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

Wyckoff Sets of Space Group R3 (No. 146) [hexagonal axes]

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

Letter Mult SS Rep. Equivalent WP
b 9 1 (x, y, z) b
a 3 3. (0, 0, z) a

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of R3 (146) [hexagonal axes] 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
2-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a b
3-y,-x,z
(
   0  -1   0    0
  -1   0   0    0
   0   0   1    0
)
m x,-x,z 
a b
4y,x,-z
(
   0   1   0    0
   1   0   0    0
   0   0  -1    0
)
2 x,x,0 
a b




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


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