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

Wyckoff Sets of Space Group P32 (No. 145)

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

Letter Mult SS Rep. Equivalent WP
a 3 1 (x, y, z) a

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Transformation of the Wyckoff Positions of P32 (145) 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
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
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
4-x,-y,z
(
  -1   0   0    0
   0  -1   0    0
   0   0   1    0
)
2 0,0,z 
a
5-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
6-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
7y,x,-z
(
   0   1   0    0
   1   0   0    0
   0   0  -1    0
)
2 x,x,0 
a
8y+2/3,x+1/3,-z
(
   0   1   0   2/3
   1   0   0   1/3
   0   0  -1    0
)
2 (1/2,1/2,0) x,x-1/6,0 
a
9y+1/3,x+2/3,-z
(
   0   1   0   1/3
   1   0   0   2/3
   0   0  -1    0
)
2 (1/2,1/2,0) x,x+1/6,0 
a
10-y,-x,-z
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1    0
)
2 x,-x,0 
a
11-y+2/3,-x+1/3,-z
(
   0  -1   0   2/3
  -1   0   0   1/3
   0   0  -1    0
)
2 (1/6,-1/6,0) x,-x+1/2,0 
a
12-y+1/3,-x+2/3,-z
(
   0  -1   0   1/3
  -1   0   0   2/3
   0   0  -1    0
)
2 (-1/6,1/6,0) x,-x+1/2,0 
a




Additional traslations generators


No. # Continuous TranslationsGeometrical Interpretation Transformed WP
1 x,y,z+t
(
   1   0   0    0
   0   1   0    0
   0   0   1    t
)
t (0,0,t) 
a


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