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

Wyckoff Sets of Space Group P-421c (No. 114)

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

Letter Mult SS Rep. Equivalent WP
e 8 1 (x, y, z) e
d 4 2.. (0, 1/2 , z) d
c 4 2.. (0, 0, z) c
b 2 -4.. (0, 0, 1/2 ) ab
a 2 -4.. (0, 0, 0) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P-421c (114) under the coset representatives of its affine normalizer


The affine normalizer coincides with the Euclidean one.

Index: 8

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+1/2,y+1/2,z
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)
t (1/2,1/2,0) 
b a c d e
3x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
t (0,0,1/2) 
b a c d e
4x+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 c d e
5-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a b c d e
6-x+1/2,-y+1/2,-z
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1    0
)
-1 1/4,1/4,0 
b a c d e
7-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 c d e
8-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 c d e


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