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

Wyckoff Sets of Space Group Immm (No. 71)

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

Letter Mult SS Rep. Equivalent WP under
Euclidean normalizer		 Equivalent WP under
affine normalizer
o 16 1 (x, y, z) o o
n 8 ..m (x, y, 0) n lmn
m 8 .m. (x, 0, z) m lmn
l 8 m.. (0, y, z) l lmn
k 8 -1 (1/4 , 1/4 , 1/4 ) k k
j 4 mm2 (1/2 , 0, z) ij efghij
i 4 mm2 (0, 0, z) ij efghij
h 4 m2m (0, y, 1/2 ) efgh efghij
g 4 m2m (0, y, 0) efgh efghij
f 4 2mm (x, 1/2 , 0) efgh efghij
e 4 2mm (x, 0, 0) efgh efghij
d 2 mmm (1/2 , 0, 1/2 ) abcd abcd
c 2 mmm (1/2 , 1/2 , 0) abcd abcd
b 2 mmm (0, 1/2 , 1/2 ) abcd abcd
a 2 mmm (0, 0, 0) abcd abcd

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of Immm (071) under the coset representatives of its affine normalizer


Index: 24

No. # Coset Representative Transformed WP
1x,y,z
(
   1   0   0    0
   0   1   0    0
   0   0   1    0
)
 
a b c d e f g h i j k l m n o
2z,x,y
(
   0   0   1    0
   1   0   0    0
   0   1   0    0
)
 
a c d b i j e f g h k n l m o
3y,z,x
(
   0   1   0    0
   0   0   1    0
   1   0   0    0
)
 
a d b c g h i j e f k m n l o
4y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
 
a d c b g h e f i j k m l n o
5z,y,x
(
   0   0   1    0
   0   1   0    0
   1   0   0    0
)
 
a c b d i j g h e f k n m l o
6x,z,y
(
   1   0   0    0
   0   0   1    0
   0   1   0    0
)
 
a b d c e f i j g h k l n m o
7x+1/2,y,z
(
   1   0   0   1/2
   0   1   0    0
   0   0   1    0
)
 
b a d c e f h g j i k l m n o
8z+1/2,x,y
(
   0   0   1   1/2
   1   0   0    0
   0   1   0    0
)
 
c a b d i j f e h g k n l m o
9y+1/2,z,x
(
   0   1   0   1/2
   0   0   1    0
   1   0   0    0
)
 
d a c b g h j i f e k m n l o
10y+1/2,x,z
(
   0   1   0   1/2
   1   0   0    0
   0   0   1    0
)
 
d a b c g h f e j i k m l n o
11z+1/2,y,x
(
   0   0   1   1/2
   0   1   0    0
   1   0   0    0
)
 
c a d b i j h g f e k n m l o
12x+1/2,z,y
(
   1   0   0   1/2
   0   0   1    0
   0   1   0    0
)
 
b a c d e f j i h g k l n m o
13x,y+1/2,z
(
   1   0   0    0
   0   1   0   1/2
   0   0   1    0
)
 
d c b a f e g h j i k l m n o
14z,x+1/2,y
(
   0   0   1    0
   1   0   0   1/2
   0   1   0    0
)
 
b d c a j i e f h g k n l m o
15y,z+1/2,x
(
   0   1   0    0
   0   0   1   1/2
   1   0   0    0
)
 
c b d a h g i j f e k m n l o
16y,x+1/2,z
(
   0   1   0    0
   1   0   0   1/2
   0   0   1    0
)
 
b c d a h g e f j i k m l n o
17z,y+1/2,x
(
   0   0   1    0
   0   1   0   1/2
   1   0   0    0
)
 
d b c a j i g h f e k n m l o
18x,z+1/2,y
(
   1   0   0    0
   0   0   1   1/2
   0   1   0    0
)
 
c d b a f e i j h g k l n m o
19x+1/2,y+1/2,z
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)
 
c d a b f e h g i j k l m n o
20z+1/2,x+1/2,y
(
   0   0   1   1/2
   1   0   0   1/2
   0   1   0    0
)
 
d b a c j i f e g h k n l m o
21y+1/2,z+1/2,x
(
   0   1   0   1/2
   0   0   1   1/2
   1   0   0    0
)
 
b c a d h g j i e f k m n l o
22y+1/2,x+1/2,z
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1    0
)
 
c b a d h g f e i j k m l n o
23z+1/2,y+1/2,x
(
   0   0   1   1/2
   0   1   0   1/2
   1   0   0    0
)
 
b d a c j i h g e f k n m l o
24x+1/2,z+1/2,y
(
   1   0   0   1/2
   0   0   1   1/2
   0   1   0    0
)
 
d c a b f e j i g h k l n m o


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