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

Wyckoff Sets of Space Group P42/mnm (No. 136)

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

Letter Mult SS Rep. Equivalent WP
k 16 1 (x, y, z) k
j 8 ..m (x, x, z) j
i 8 m.. (x, y, 0) i
h 8 2.. (0, 1/2 , z) h
g 4 m.2 m (x, - x, 0) fg
f 4 m.2 m (x, x, 0) fg
e 4 2.m m (0, 0, z) e
d 4 -4.. (0, 1/2 , 1/4 ) d
c 4 2/m.. (0, 1/2 , 0) c
b 2 m.m m (0, 0, 1/2 ) ab
a 2 m.m m (0, 0, 0) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P42/mnm (136) 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
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 h 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) 
b a c d e g f 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) 
a b c d e g f h i j k


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