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

Wyckoff Sets of Space Group P321 (No. 150)

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

Letter Mult SS Rep. Equivalent WP
g 6 1 (x, y, z) g
f 3 .2. (x, 0, 1/2 ) ef
e 3 .2. (x, 0, 0) ef
d 2 3.. (1/3 , 2/3 , z) d
c 2 3.. (0, 0, z) c
b 1 32. (0, 0, 1/2 ) ab
a 1 32. (0, 0, 0) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P321 (150) under the coset representatives of its affine normalizer


The affine normalizer coincides with the Euclidean one.

Index: 8

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
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 d f e g
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
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 c d f e g
5-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
6-x,-y,-z+1/2
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1   1/2
)
-1 0,0,1/4 
b a c d f e g
7x,y,-z
(
   1   0   0    0
   0   1   0    0
   0   0  -1    0
)
m x,y,0 
a b c d e f g
8x,y,-z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0  -1   1/2
)
m x,y,1/4 
b a c d f e g


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