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

Wyckoff Sets of Space Group P42/nmc (No. 137) [origin choice 2]

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

Letter Mult SS Rep. Equivalent WP
h 16 1 (x, y, z) h
g 8 .m. (1/4 , y, z) g
f 8 ..2 (x, - x, 1/4 ) f
e 8 -1 (0, 0, 0) e
d 4 2mm . (1/4 , 1/4 , z) d
c 4 2mm . (3/4 , 1/4 , z) c
b 2 -4m2 (3/4 , 1/4 , 1/4 ) ab
a 2 -4m2 (3/4 , 1/4 , 3/4 ) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P42/nmc (137) [origin choice 2] 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
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
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 f g h
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 f g h


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