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

Wyckoff Sets of Space Group P432 (No. 207)

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

Letter Mult SS Rep. Equivalent WP
k 24 1 (x, y, z) k
j 12 ..2 (1/2 , y, y) ij
i 12 ..2 (0, y, y) ij
h 12 2.. (x, 1/2 , 0) h
g 8 .3. (x, x, x) g
f 6 4.. (x, 1/2 , 1/2 ) ef
e 6 4.. (x, 0, 0) ef
d 3 42. 2 (1/2 , 0, 0) cd
c 3 42. 2 (0, 1/2 , 1/2 ) cd
b 1 432 (1/2 , 1/2 , 1/2 ) ab
a 1 432 (0, 0, 0) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P432 (207) 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 e f g h i j k
2x+1/2,y+1/2,z+1/2
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1   1/2
)
t (1/2,1/2,1/2) 
b a d c f e g h j i k
3-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a b c d e f g h i j k
4-x+1/2,-y+1/2,-z+1/2
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1   1/2
)
-1 1/4,1/4,1/4 
b a d c f e g h j i k


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