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

Wyckoff Sets of Space Group P6322 (No. 182)

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

Letter Mult SS Rep. Equivalent WP
i 12 1 (x, y, z) i
h 6 ..2 (x, 2x, 1/4 ) h
g 6 .2. (x, 0, 0) g
f 4 3.. (1/3 , 2/3 , z) f
e 4 3.. (0, 0, z) e
d 2 3.2 (1/3 , 2/3 , 3/4 ) cd
c 2 3.2 (1/3 , 2/3 , 1/4 ) cd
b 2 3.2 (0, 0, 1/4 ) b
a 2 32. (0, 0, 0) a

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P6322 (182) 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 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) 
a b d c e f g h i
3-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a b c d e f g h i
4-x,-y,-z+1/2
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1   1/2
)
-1 0,0,1/4 
a b d c e f g h i


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