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

Wyckoff Sets of Space Group I41/a (No. 88) [origin choice 2]

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

Letter Mult SS Rep. Equivalent WP
f 16 1 (x, y, z) f
e 8 2.. (0, 1/4 , z) e
d 8 -1 (0, 0, 1/2 ) cd
c 8 -1 (0, 0, 0) cd
b 4 -4.. (0, 1/4 , 5/8 ) ab
a 4 -4.. (0, 1/4 , 1/8 ) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of I41/a (088) [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
2x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
t (0,0,1/2) 
b a d c e f
3y+1/4,x+1/4,z+1/4
(
   0   1   0   1/4
   1   0   0   1/4
   0   0   1   1/4
)
d (1/4,1/4,1/4) x,x,z 
a b c d e f
4y+1/4,x+1/4,z+3/4
(
   0   1   0   1/4
   1   0   0   1/4
   0   0   1   3/4
)
d (1/4,1/4,3/4) x,x,z 
b a d c e f


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