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

Wyckoff Sets of Space Group I-42m (No. 121)

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

Letter Mult SS Rep. Equivalent WP
j 16 1 (x, y, z) j
i 8 ..m (x, x, z) i
h 8 2.. (0, 1/2 , z) h
g 8 .2. (x, 0, 1/2 ) fg
f 8 .2. (x, 0, 0) fg
e 4 2.m m (0, 0, z) e
d 4 -4.. (0, 1/2 , 1/4 ) d
c 4 222 . (0, 1/2 , 0) c
b 2 -42m (0, 0, 1/2 ) ab
a 2 -42m (0, 0, 0) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of I-42m (121) 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
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 c d e g f h i j
3-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a b c d e f g h i j
4-x,-y,-z+1/2
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1   1/2
)
-1 0,0,1/4 
b a c d e g f h i j


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