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

Wyckoff Sets of Space Group P-31m (No. 162)

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

Letter Mult SS Rep. Equivalent WP
l 12 1 (x, y, z) l
k 6 ..m (x, 0, z) k
j 6 ..2 (x, - x, 1/2 ) ij
i 6 ..2 (x, - x, 0) ij
h 4 3.. (1/3 , 2/3 , z) h
g 3 ..2/m (1/2 , 0, 1/2 ) fg
f 3 ..2/m (1/2 , 0, 0) fg
e 2 3.m (0, 0, z) e
d 2 3.2 (1/3 , 2/3 , 1/2 ) cd
c 2 3.2 (1/3 , 2/3 , 0) cd
b 1 -3.m (0, 0, 1/2 ) ab
a 1 -3.m (0, 0, 0) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P-31m (162) 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 j k l
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 d c e g f h j i k l
3-x,-y,z
(
  -1   0   0    0
   0  -1   0    0
   0   0   1    0
)
2 0,0,z 
a b c d e f g h i j k l
4-x,-y,z+1/2
(
  -1   0   0    0
   0  -1   0    0
   0   0   1   1/2
)
2 (0,0,1/2) 0,0,z 
b a d c e g f h j i k l


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