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

Wyckoff Sets of Space Group P-43n (No. 218)

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

Letter Mult SS Rep. Equivalent WP
i 24 1 (x, y, z) i
h 12 2.. (x, 0, 1/2 ) gh
g 12 2.. (x, 1/2 , 0) gh
f 12 2.. (x, 0, 0) f
e 8 .3. (x, x, x) e
d 6 -4.. (1/4 , 0, 1/2 ) cd
c 6 -4.. (1/4 , 1/2 , 0) cd
b 6 222 . . (0, 1/2 , 1/2 ) b
a 2 23. (0, 0, 0) a

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P-43n (218) under the coset representatives of its affine normalizer


The affine normalizer coincides with the Euclidean one.

Index: 4

No. # Coset RepresentativeGeometrical Interpretation Transformed WP
1 x,y,z
(
   1   0   0    0
   0   1   0    0
   0   0   1    0
)
1 
a b c d e f g h i
2 x+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) 
a b d c e f h g i
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
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 
a b d c e f h g i


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