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

Wyckoff Sets of Space Group Pm-3n (No. 223)

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

Letter Mult SS Rep. Equivalent WP
l 48 1 (x, y, z) l
k 24 m.. (0, y, z) k
j 24 ..2 (1/4 , y, y + 1/2 ) j
i 16 .3. (x, x, x) i
h 12 mm2 . . (x, 1/2 , 0) gh
g 12 mm2 . . (x, 0, 1/2 ) gh
f 12 mm2 . . (x, 0, 0) f
e 8 .32 (1/4 , 1/4 , 1/4 ) e
d 6 -4m. 2 (1/4 , 1/2 , 0) cd
c 6 -4m. 2 (1/4 , 0, 1/2 ) cd
b 6 mmm . . (0, 1/2 , 1/2 ) b
a 2 m-3. (0, 0, 0) a

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of Pm-3n (223) under the coset representatives of its affine normalizer


The affine normalizer coincides with the Euclidean one.

Index: 2

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
2x+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 h g i j k l


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