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

Wyckoff Sets of Space Group P312 (No. 149)

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

Letter Mult SS Rep. Equivalent WP
l 6 1 (x, y, z) l
k 3 ..2 (x, - x, 1/2 ) jk
j 3 ..2 (x, - x, 0) jk
i 2 3.. (2/3 , 1/3 , z) ghi
h 2 3.. (1/3 , 2/3 , z) ghi
g 2 3.. (0, 0, z) ghi
f 1 3.2 (2/3 , 1/3 , 1/2 ) abcdef
e 1 3.2 (2/3 , 1/3 , 0) abcdef
d 1 3.2 (1/3 , 2/3 , 1/2 ) abcdef
c 1 3.2 (1/3 , 2/3 , 0) abcdef
b 1 3.2 (0, 0, 1/2 ) abcdef
a 1 3.2 (0, 0, 0) abcdef

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P312 (149) 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 e f g h i j k l
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) 
c d e f a b h i g j k l
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) 
e f a b c d i g h j k l
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 d c f e g h i k j l
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) 
d c f e b a h i g k j l
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) 
f e b a d c i g h k j l
7-x,-y,z
(
  -1   0   0    0
   0  -1   0    0
   0   0   1    0
)
2 0,0,z 
a b e f c d g i h j k l
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 
e f c d a b i h g j k l
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 
c d a b e f h g i j k l
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 f e d c g i h k j l
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 
f e d c b a i h g k j l
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 
d c b a f e h g i k j l
13-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a b e f c d g i h j k l
14-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 
e f c d a b i h g j k l
15-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 
c d a b e f h g i j k l
16-x,-y,-z+1/2
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1   1/2
)
-1 0,0,1/4 
b a f e d c g i h k j l
17-x+2/3,-y+1/3,-z+1/2
(
  -1   0   0   2/3
   0  -1   0   1/3
   0   0  -1   1/2
)
-1 1/3,1/6,1/4 
f e d c b a i h g k j l
18-x+1/3,-y+2/3,-z+1/2
(
  -1   0   0   1/3
   0  -1   0   2/3
   0   0  -1   1/2
)
-1 1/6,1/3,1/4 
d c b a f e h g i k j l
19x,y,-z
(
   1   0   0    0
   0   1   0    0
   0   0  -1    0
)
m x,y,0 
a b c d e f g h i j k l
20x+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 
c d e f a b h i g j k l
21x+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 
e f a b c d i g h j k l
22x,y,-z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0  -1   1/2
)
m x,y,1/4 
b a d c f e g h i k j l
23x+2/3,y+1/3,-z+1/2
(
   1   0   0   2/3
   0   1   0   1/3
   0   0  -1   1/2
)
g (2/3,1/3,0) x,y,1/4 
d c f e b a h i g k j l
24x+1/3,y+2/3,-z+1/2
(
   1   0   0   1/3
   0   1   0   2/3
   0   0  -1   1/2
)
g (1/3,2/3,0) x,y,1/4 
f e b a d c i g h k j l


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