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

Wyckoff Sets of Space Group P42/nbc (No. 133) [origin choice 2]

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 ..2 (x, x, 1/4 ) j
i 8 .2. (x, 1/4 , 1/2 ) hi
h 8 .2. (x, 1/4 , 0) hi
g 8 2.. (3/4 , 1/4 , z) g
f 8 2.. (1/4 , 1/4 , z) f
e 8 -1 (0, 0, 0) e
d 4 -4.. (3/4 , 1/4 , 3/4 ) d
c 4 2.2 2 (1/4 , 1/4 , 1/4 ) c
b 4 222 . (3/4 , 1/4 , 0) b
a 4 222 . (1/4 , 1/4 , 0) a

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P42/nbc (133) [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 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) 
a b 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) 
a b c d e f g i h 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 f g i h j k


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