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

Wyckoff Sets of Space Group P42/mcm (No. 132)

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

Letter Mult SS Rep. Equivalent WP
p 16 1 (x, y, z) p
o 8 ..m (x, x, z) o
n 8 m.. (x, y, 0) n
m 8 .2. (x, 1/2 , 1/4 ) lm
l 8 .2. (x, 0, 1/4 ) lm
k 8 2.. (0, 1/2 , z) k
j 4 m.2 m (x, x, 1/2 ) ij
i 4 m.2 m (x, x, 0) ij
h 4 2.m m (1/2 , 1/2 , z) gh
g 4 2.m m (0, 0, z) gh
f 4 2/m.. (0, 1/2 , 0) f
e 4 222 . (0, 1/2 , 1/4 ) e
d 2 -42m (1/2 , 1/2 , 1/4 ) bd
c 2 m.m m (1/2 , 1/2 , 0) ac
b 2 -42m (0, 0, 1/4 ) bd
a 2 m.m m (0, 0, 0) ac

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P42/mcm (132) 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 l m n o p
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) 
c d a b e f h g i j k m l n o p
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 c d e f g h j i k l m n o p
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) 
c d a b e f h g j i k m l n o p


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