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

Wyckoff Sets of Space Group P42/n (No. 86) [origin choice 2]

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

Letter Mult SS Rep. Equivalent WP
g 8 1 (x, y, z) g
f 4 2.. (1/4 , 1/4 , z) f
e 4 2.. (3/4 , 1/4 , z) e
d 4 -1 (0, 0, 1/2 ) cd
c 4 -1 (0, 0, 0) cd
b 2 -4.. (1/4 , 1/4 , 3/4 ) ab
a 2 -4.. (1/4 , 1/4 , 1/4 ) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P42/n (086) [origin choice 2] 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 f g
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 f g
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 d c e f g
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 d c e f g
5y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
m x,x,z 
a b c d e f g
6y+1/2,x+1/2,z
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1    0
)
g (1/2,1/2,0) x,x,z 
b a c d e f g
7y,x,z+1/2
(
   0   1   0    0
   1   0   0    0
   0   0   1   1/2
)
c x,x,z 
b a d c e f g
8y+1/2,x+1/2,z+1/2
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1   1/2
)
n (1/2,1/2,1/2) x,x,z 
a b d c e f g


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