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

Wyckoff Sets of Space Group P31m (No. 157)

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

Letter Mult SS Rep. Equivalent WP
d 6 1 (x, y, z) d
c 3 ..m (x, 0, z) c
b 2 3.. (1/3 , 2/3 , z) b
a 1 3.m (0, 0, z) a

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P31m (157) 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
2-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a b c d
3-x,-y,z
(
  -1   0   0    0
   0  -1   0    0
   0   0   1    0
)
2 0,0,z 
a b c d
4x,y,-z
(
   1   0   0    0
   0   1   0    0
   0   0  -1    0
)
m x,y,0 
a b c d




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 b c d


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