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

Wyckoff Sets of Space Group P3 (No. 143)

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

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

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P3 (143) under the coset representatives of its affine normalizer


The affine normalizer coincides with the Euclidean one.

Index: 24 · (∞)

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
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
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
4-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a c b d
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
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
7-x,-y,z
(
  -1   0   0    0
   0  -1   0    0
   0   0   1    0
)
2 0,0,z 
a c b d
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
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
10x,y,-z
(
   1   0   0    0
   0   1   0    0
   0   0  -1    0
)
m x,y,0 
a b c d
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
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
13y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
m x,x,z 
a c b d
14y+2/3,x+1/3,z
(
   0   1   0   2/3
   1   0   0   1/3
   0   0   1    0
)
g (1/2,1/2,0) x+1/6,x,z 
c b a d
15y+1/3,x+2/3,z
(
   0   1   0   1/3
   1   0   0   2/3
   0   0   1    0
)
g (1/2,1/2,0) x-1/6,x,z 
b a c d
16-y,-x,-z
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1    0
)
2 x,-x,0 
a b c d
17-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 
b c a d
18-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 
c a b d
19-y,-x,z
(
   0  -1   0    0
  -1   0   0    0
   0   0   1    0
)
m x,-x,z 
a b c d
20-y+2/3,-x+1/3,z
(
   0  -1   0   2/3
  -1   0   0   1/3
   0   0   1    0
)
g (1/6,-1/6,0) x+1/2,-x,z 
b c a d
21-y+1/3,-x+2/3,z
(
   0  -1   0   1/3
  -1   0   0   2/3
   0   0   1    0
)
g (-1/6,1/6,0) x+1/2,-x,z 
c a b d
22y,x,-z
(
   0   1   0    0
   1   0   0    0
   0   0  -1    0
)
2 x,x,0 
a c b d
23y+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 
b a c d
24y+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 
c b a 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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