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

Wyckoff Sets of Space Group Pn-3 (No. 201) [origin choice 2]

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

Letter Mult SS Rep. Equivalent WP
h 24 1 (x, y, z) h
g 12 2.. (x, 3/4 , 1/4 ) g
f 12 2.. (x, 1/4 , 1/4 ) f
e 8 .3. (x, x, x) e
d 6 222 . . (1/4 , 3/4 , 3/4 ) d
c 4 .-3. (1/2 , 1/2 , 1/2 ) bc
b 4 .-3. (0, 0, 0) bc
a 2 23. (1/4 , 1/4 , 1/4 ) a

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of Pn-3 (201) [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+1/2
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1   1/2
)
t (1/2,1/2,1/2) 
a c b d e f g h
3y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
m x,x,z 
a b c d e f g h
4y+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 
a c b d e f g h


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