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

Wyckoff Sets of Space Group P3m1 (No. 156)

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

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

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P3m1 (156) 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 d e
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) 
b c a d e
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) 
c a b d e
4-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a c b d e
5-x+2/3,-y+1/3,-z
(
  -1   0   0   2/3
   0  -1   0   1/3
   0   0  -1    0
)
-1 1/3,1/6,0 
c b a d e
6-x+1/3,-y+2/3,-z
(
  -1   0   0   1/3
   0  -1   0   2/3
   0   0  -1    0
)
-1 1/6,1/3,0 
b a c d e
7-x,-y,z
(
  -1   0   0    0
   0  -1   0    0
   0   0   1    0
)
2 0,0,z 
a c b d e
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 
c b a d e
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 
b a c d e
10x,y,-z
(
   1   0   0    0
   0   1   0    0
   0   0  -1    0
)
m x,y,0 
a b c d e
11x+2/3,y+1/3,-z
(
   1   0   0   2/3
   0   1   0   1/3
   0   0  -1    0
)
g (2/3,1/3,0) x,y,0 
b c a d e
12x+1/3,y+2/3,-z
(
   1   0   0   1/3
   0   1   0   2/3
   0   0  -1    0
)
g (1/3,2/3,0) x,y,0 
c a b d e




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 e


Bilbao Crystallographic Server
http://www.cryst.ehu.es 		For comments, please mail to
administrador.bcs@ehu.eus