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

Wyckoff Sets of Space Group P3212 (No. 153)

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

Letter Mult SS Rep. Equivalent WP
c 6 1 (x, y, z) c
b 3 ..2 (x, - x, 1/6 ) ab
a 3 ..2 (x, - x, 2/3 ) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P3212 (153) under the coset representatives of its affine normalizer


The affine normalizer coincides with the Euclidean one.

Index: 12

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
2x+2/3,y+1/3,z
(
   1   0   0   2/3
   0   1   0   1/3
   0   0   1    0
)
t (2/3,1/3,0) 
a b c
3x+1/3,y+2/3,z
(
   1   0   0   1/3
   0   1   0   2/3
   0   0   1    0
)
t (1/3,2/3,0) 
a b c
4x,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
5x+2/3,y+1/3,z+1/2
(
   1   0   0   2/3
   0   1   0   1/3
   0   0   1   1/2
)
t (2/3,1/3,1/2) 
b a c
6x+1/3,y+2/3,z+1/2
(
   1   0   0   1/3
   0   1   0   2/3
   0   0   1   1/2
)
t (1/3,2/3,1/2) 
b a c
7-x,-y,z
(
  -1   0   0    0
   0  -1   0    0
   0   0   1    0
)
2 0,0,z 
a b c
8-x+2/3,-y+1/3,z
(
  -1   0   0   2/3
   0  -1   0   1/3
   0   0   1    0
)
2 1/3,1/6,z 
a b c
9-x+1/3,-y+2/3,z
(
  -1   0   0   1/3
   0  -1   0   2/3
   0   0   1    0
)
2 1/6,1/3,z 
a b c
10-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
11-x+2/3,-y+1/3,z+1/2
(
  -1   0   0   2/3
   0  -1   0   1/3
   0   0   1   1/2
)
2 (0,0,1/2) 1/3,1/6,z 
b a c
12-x+1/3,-y+2/3,z+1/2
(
  -1   0   0   1/3
   0  -1   0   2/3
   0   0   1   1/2
)
2 (0,0,1/2) 1/6,1/3,z 
b a c


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