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

Wyckoff Sets of Space Group R-3 (No. 148) [hexagonal axes]

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

Letter Mult SS Rep. Equivalent WP
f 18 1 (x, y, z) f
e 9 -1 (1/2 , 0, 0) de
d 9 -1 (1/2 , 0, 1/2 ) de
c 6 3. (0, 0, z) c
b 3 -3. (0, 0, 1/2 ) ab
a 3 -3. (0, 0, 0) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of R-3 (148) [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 c d e f
2x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
t (0,0,1/2) 
b a c e d f
3-y,-x,z
(
   0  -1   0    0
  -1   0   0    0
   0   0   1    0
)
m x,-x,z 
a b c d e f
4-y,-x,z+1/2
(
   0  -1   0    0
  -1   0   0    0
   0   0   1   1/2
)
c x,-x,z 
b a c e d f


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