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

Wyckoff Sets of Space Group P42/m (No. 84)

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

Letter Mult SS Rep. Equivalent WP
k 8 1 (x, y, z) k
j 4 m.. (x, y, 0) j
i 4 2.. (0, 1/2 , z) i
h 4 2.. (1/2 , 1/2 , z) gh
g 4 2.. (0, 0, z) gh
f 2 -4.. (1/2 , 1/2 , 1/4 ) ef
e 2 -4.. (0, 0, 1/4 ) ef
d 2 2/m.. (0, 1/2 , 1/2 ) cd
c 2 2/m.. (0, 1/2 , 0) cd
b 2 2/m.. (1/2 , 1/2 , 0) ab
a 2 2/m.. (0, 0, 0) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P42/m (084) 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 h i j k
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 d c f e h g i j k
3x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
t (0,0,1/2)
a b d c e f g h i j k
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)
b a c d f e h g i j k
5y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
m x,x,z
a b d c e f g h i j k
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 f e h g i j k
7y,x,z+1/2
(
   0   1   0    0
   1   0   0    0
   0   0   1   1/2
)
c x,x,z
a b c d e f g h i j k
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
b a d c f e h g i j k


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