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

Wyckoff Sets of Space Group P-42m (No. 111)

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

Letter Mult SS Rep. Equivalent WP
o 8 1 (x, y, z) o
n 4 ..m (x, x, z) n
m 4 2.. (0, 1/2 , z) m
l 4 .2. (x, 1/2 , 0) ijkl
k 4 .2. (x, 0, 1/2 ) ijkl
j 4 .2. (x, 1/2 , 1/2 ) ijkl
i 4 .2. (x, 0, 0) ijkl
h 2 2.m m (1/2 , 1/2 , z) gh
g 2 2.m m (0, 0, z) gh
f 2 222 . (1/2 , 0, 1/2 ) ef
e 2 222 . (1/2 , 0, 0) ef
d 1 -42m (1/2 , 1/2 , 0) abcd
c 1 -42m (0, 0, 1/2 ) abcd
b 1 -42m (1/2 , 1/2 , 1/2 ) abcd
a 1 -42m (0, 0, 0) abcd

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P-42m (111) under the coset representatives of its affine normalizer


The affine normalizer coincides with the Euclidean one.

Index: 8

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 m n o
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) 
d c b a e f h g l k j i m n o
3x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
t (0,0,1/2) 
c d a b f e g h k l i j m n o
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) 
b a d c f e h g j i l k m n o
5-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 k l m n o
6-x+1/2,-y+1/2,-z
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1    0
)
-1 1/4,1/4,0 
d c b a e f h g l k j i m n o
7-x,-y,-z+1/2
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1   1/2
)
-1 0,0,1/4 
c d a b f e g h k l i j m n o
8-x+1/2,-y+1/2,-z+1/2
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1   1/2
)
-1 1/4,1/4,1/4 
b a d c f e h g j i l k m n o


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