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

Wyckoff Sets of Space Group R-3m (No. 166) [hexagonal axes]

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

Letter Mult SS Rep. Equivalent WP
i 36 1 (x, y, z) i
h 18 .m (x, - x, z) h
g 18 .2 (x, 0, 1/2 ) fg
f 18 .2 (x, 0, 0) fg
e 9 .2/m (1/2 , 0, 0) de
d 9 .2/m (1/2 , 0, 1/2 ) de
c 6 3m (0, 0, z) c
b 3 -3m (0, 0, 1/2 ) ab
a 3 -3m (0, 0, 0) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of R-3m (166) [hexagonal axes] under the coset representatives of its affine normalizer


The affine normalizer coincides with the Euclidean one.

Index: 2

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 g h i
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 g f h i


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