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

Wyckoff Sets of Space Group Pmmm (No. 47)

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
z 4 ..m (x, y, 1/2 ) wxyz uvwxyz
y 4 ..m (x, y, 0) wxyz uvwxyz
x 4 .m. (x, 1/2 , z) wxyz uvwxyz
w 4 .m. (x, 0, z) wxyz uvwxyz
v 4 m.. (1/2 , y, z) uv uvwxyz
u 4 m.. (0, y, z) uv uvwxyz
t 2 mm2 (1/2 , 1/2 , z) qrst ijklmnopqrst
s 2 mm2 (1/2 , 0, z) qrst ijklmnopqrst
r 2 mm2 (0, 1/2 , z) qrst ijklmnopqrst
q 2 mm2 (0, 0, z) qrst ijklmnopqrst
p 2 m2m (1/2 , y, 1/2 ) mnop ijklmnopqrst
o 2 m2m (1/2 , y, 0) mnop ijklmnopqrst
n 2 m2m (0, y, 1/2 ) mnop ijklmnopqrst
m 2 m2m (0, y, 0) mnop ijklmnopqrst
l 2 2mm (x, 1/2 , 1/2 ) ijkl ijklmnopqrst
k 2 2mm (x, 1/2 , 0) ijkl ijklmnopqrst
j 2 2mm (x, 0, 1/2 ) ijkl ijklmnopqrst
i 2 2mm (x, 0, 0) ijkl ijklmnopqrst
h 1 mmm (1/2 , 1/2 , 1/2 ) abcdefgh abcdefgh
g 1 mmm (0, 1/2 , 1/2 ) abcdefgh abcdefgh
f 1 mmm (1/2 , 1/2 , 0) abcdefgh abcdefgh
e 1 mmm (0, 1/2 , 0) abcdefgh abcdefgh
d 1 mmm (1/2 , 0, 1/2 ) abcdefgh abcdefgh
c 1 mmm (0, 0, 1/2 ) abcdefgh abcdefgh
b 1 mmm (1/2 , 0, 0) abcdefgh abcdefgh
a 1 mmm (0, 0, 0) abcdefgh abcdefgh
A 8 1 (x, y, z) A A

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of Pmmm (047) under the coset representatives of its affine normalizer


Index: 48

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 p q r s t u v w x y z A
2x+1/2,y,z
(
   1   0   0   1/2
   0   1   0    0
   0   0   1    0
)
 
b a d c f e h g i j k l o p m n s t q r v u w x y z A
3x,y+1/2,z
(
   1   0   0    0
   0   1   0   1/2
   0   0   1    0
)
 
e f g h a b c d k l i j m n o p r q t s u v x w y z A
4x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
 
c d a b g h e f j i l k n m p o q r s t u v w x z y A
5x+1/2,y+1/2,z
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)
 
f e h g b a d c k l i j o p m n t s r q v u x w y z A
6x+1/2,y,z+1/2
(
   1   0   0   1/2
   0   1   0    0
   0   0   1   1/2
)
 
d c b a h g f e j i l k p o n m s t q r v u w x z y A
7x,y+1/2,z+1/2
(
   1   0   0    0
   0   1   0   1/2
   0   0   1   1/2
)
 
g h e f c d a b l k j i n m p o r q t s u v x w z y A
8x+1/2,y+1/2,z+1/2
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1   1/2
)
 
h g f e d c b a l k j i p o n m t s r q v u x w z y A
9z,x,y
(
   0   0   1    0
   1   0   0    0
   0   1   0    0
)
 
a c e g b d f h q r s t i k j l m o n p y z u v w x A
10z+1/2,x,y
(
   0   0   1   1/2
   1   0   0    0
   0   1   0    0
)
 
c a g e d b h f q r s t j l i k n p m o z y u v w x A
11z,x+1/2,y
(
   0   0   1    0
   1   0   0   1/2
   0   1   0    0
)
 
b d f h a c e g s t q r i k j l o m p n y z v u w x A
12z,x,y+1/2
(
   0   0   1    0
   1   0   0    0
   0   1   0   1/2
)
 
e g a c f h b d r q t s k i l j m o n p y z u v x w A
13z+1/2,x+1/2,y
(
   0   0   1   1/2
   1   0   0   1/2
   0   1   0    0
)
 
d b h f c a g e s t q r j l i k p n o m z y v u w x A
14z+1/2,x,y+1/2
(
   0   0   1   1/2
   1   0   0    0
   0   1   0   1/2
)
 
g e c a h f d b r q t s l j k i n p m o z y u v x w A
15z,x+1/2,y+1/2
(
   0   0   1    0
   1   0   0   1/2
   0   1   0   1/2
)
 
f h b d e g a c t s r q k i l j o m p n y z v u x w A
16z+1/2,x+1/2,y+1/2
(
   0   0   1   1/2
   1   0   0   1/2
   0   1   0   1/2
)
 
h f d b g e c a t s r q l j k i p n o m z y v u x w A
17y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
 
a e c g b f d h m n o p i j k l q s r t w x u v y z A
18y+1/2,x,z
(
   0   1   0   1/2
   1   0   0    0
   0   0   1    0
)
 
e a g c f b h d m n o p k l i j r t q s x w u v y z A
19y,x+1/2,z
(
   0   1   0    0
   1   0   0   1/2
   0   0   1    0
)
 
b f d h a e c g o p m n i j k l s q t r w x v u y z A
20y,x,z+1/2
(
   0   1   0    0
   1   0   0    0
   0   0   1   1/2
)
 
c g a e d h b f n m p o j i l k q s r t w x u v z y A
21y+1/2,x+1/2,z
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1    0
)
 
f b h d e a g c o p m n k l i j t r s q x w v u y z A
22y+1/2,x,z+1/2
(
   0   1   0   1/2
   1   0   0    0
   0   0   1   1/2
)
 
g c e a h d f b n m p o l k j i r t q s x w u v z y A
23y,x+1/2,z+1/2
(
   0   1   0    0
   1   0   0   1/2
   0   0   1   1/2
)
 
d h b f c g a e p o n m j i l k s q t r w x v u z y A
24y+1/2,x+1/2,z+1/2
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1   1/2
)
 
h d f b g c e a p o n m l k j i t r s q x w v u z y A
25y,z,x
(
   0   1   0    0
   0   0   1    0
   1   0   0    0
)
 
a e b f c g d h m o n p q s r t i j k l w x y z u v A
26y+1/2,z,x
(
   0   1   0   1/2
   0   0   1    0
   1   0   0    0
)
 
e a f b g c h d m o n p r t q s k l i j x w y z u v A
27y,z+1/2,x
(
   0   1   0    0
   0   0   1   1/2
   1   0   0    0
)
 
c g d h a e b f n p m o q s r t j i l k w x z y u v A
28y,z,x+1/2
(
   0   1   0    0
   0   0   1    0
   1   0   0   1/2
)
 
b f a e d h c g o m p n s q t r i j k l w x y z v u A
29y+1/2,z+1/2,x
(
   0   1   0   1/2
   0   0   1   1/2
   1   0   0    0
)
 
g c h d e a f b n p m o r t q s l k j i x w z y u v A
30y+1/2,z,x+1/2
(
   0   1   0   1/2
   0   0   1    0
   1   0   0   1/2
)
 
f b e a h d g c o m p n t r s q k l i j x w y z v u A
31y,z+1/2,x+1/2
(
   0   1   0    0
   0   0   1   1/2
   1   0   0   1/2
)
 
d h c g b f a e p n o m s q t r j i l k w x z y v u A
32y+1/2,z+1/2,x+1/2
(
   0   1   0   1/2
   0   0   1   1/2
   1   0   0   1/2
)
 
h d g c f b e a p n o m t r s q l k j i x w z y v u A
33z,y,x
(
   0   0   1    0
   0   1   0    0
   1   0   0    0
)
 
a c b d e g f h q s r t m o n p i k j l y z w x u v A
34z+1/2,y,x
(
   0   0   1   1/2
   0   1   0    0
   1   0   0    0
)
 
c a d b g e h f q s r t n p m o j l i k z y w x u v A
35z,y+1/2,x
(
   0   0   1    0
   0   1   0   1/2
   1   0   0    0
)
 
e g f h a c b d r t q s m o n p k i l j y z x w u v A
36z,y,x+1/2
(
   0   0   1    0
   0   1   0    0
   1   0   0   1/2
)
 
b d a c f h e g s q t r o m p n i k j l y z w x v u A
37z+1/2,y+1/2,x
(
   0   0   1   1/2
   0   1   0   1/2
   1   0   0    0
)
 
g e h f c a d b r t q s n p m o l j k i z y x w u v A
38z+1/2,y,x+1/2
(
   0   0   1   1/2
   0   1   0    0
   1   0   0   1/2
)
 
d b c a h f g e s q t r p n o m j l i k z y w x v u A
39z,y+1/2,x+1/2
(
   0   0   1    0
   0   1   0   1/2
   1   0   0   1/2
)
 
f h e g b d a c t r s q o m p n k i l j y z x w v u A
40z+1/2,y+1/2,x+1/2
(
   0   0   1   1/2
   0   1   0   1/2
   1   0   0   1/2
)
 
h f g e d b c a t r s q p n o m l j k i z y x w v u A
41x,z,y
(
   1   0   0    0
   0   0   1    0
   0   1   0    0
)
 
a b e f c d g h i k j l q r s t m n o p u v y z w x A
42x+1/2,z,y
(
   1   0   0   1/2
   0   0   1    0
   0   1   0    0
)
 
b a f e d c h g i k j l s t q r o p m n v u y z w x A
43x,z+1/2,y
(
   1   0   0    0
   0   0   1   1/2
   0   1   0    0
)
 
c d g h a b e f j l i k q r s t n m p o u v z y w x A
44x,z,y+1/2
(
   1   0   0    0
   0   0   1    0
   0   1   0   1/2
)
 
e f a b g h c d k i l j r q t s m n o p u v y z x w A
45x+1/2,z+1/2,y
(
   1   0   0   1/2
   0   0   1   1/2
   0   1   0    0
)
 
d c h g b a f e j l i k s t q r p o n m v u z y w x A
46x+1/2,z,y+1/2
(
   1   0   0   1/2
   0   0   1    0
   0   1   0   1/2
)
 
f e b a h g d c k i l j t s r q o p m n v u y z x w A
47x,z+1/2,y+1/2
(
   1   0   0    0
   0   0   1   1/2
   0   1   0   1/2
)
 
g h c d e f a b l j k i r q t s n m p o u v z y x w A
48x+1/2,z+1/2,y+1/2
(
   1   0   0   1/2
   0   0   1   1/2
   0   1   0   1/2
)
 
h g d c f e b a l j k i t s r q p o n m v u z y x w A


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