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

Wyckoff Sets of Space Group Pnnn (No. 48) [origin choice 2]

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
m 8 1 (x, y, z) m m
l 4 ..2 (1/4 , 3/4 , z) kl ghijkl
k 4 ..2 (1/4 , 1/4 , z) kl ghijkl
j 4 .2. (3/4 , y, 1/4 ) ij ghijkl
i 4 .2. (1/4 , y, 1/4 ) ij ghijkl
h 4 2.. (x, 1/4 , 3/4 ) gh ghijkl
g 4 2.. (x, 1/4 , 1/4 ) gh ghijkl
f 4 -1 (0, 0, 0) ef ef
e 4 -1 (1/2 , 1/2 , 1/2 ) ef ef
d 2 222 (1/4 , 3/4 , 1/4 ) abcd abcd
c 2 222 (1/4 , 1/4 , 3/4 ) abcd abcd
b 2 222 (3/4 , 1/4 , 1/4 ) abcd abcd
a 2 222 (1/4 , 1/4 , 1/4 ) abcd abcd

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of Pnnn (048) [origin choice 2] 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
2x+1/2,y,z
(
   1   0   0   1/2
   0   1   0    0
   0   0   1    0
)
 
b a d c f e g h j i l k m
3x,y+1/2,z
(
   1   0   0    0
   0   1   0   1/2
   0   0   1    0
)
 
d c b a f e h g i j l k m
4x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
 
c d a b f e h g j i k l m
5x+1/2,y+1/2,z
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)
 
c d a b e f h g j i k l m
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 e f h g i j l k m
7x,y+1/2,z+1/2
(
   1   0   0    0
   0   1   0   1/2
   0   0   1   1/2
)
 
b a d c e f g h j i l k m
8x+1/2,y+1/2,z+1/2
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1   1/2
)
 
a b c d f e g h i j k l m
9z,x,y
(
   0   0   1    0
   1   0   0    0
   0   1   0    0
)
 
a c d b e f k l g h i j m
10z+1/2,x,y
(
   0   0   1   1/2
   1   0   0    0
   0   1   0    0
)
 
c a b d f e k l h g j i m
11z,x+1/2,y
(
   0   0   1    0
   1   0   0   1/2
   0   1   0    0
)
 
b d c a f e l k g h j i m
12z,x,y+1/2
(
   0   0   1    0
   1   0   0    0
   0   1   0   1/2
)
 
d b a c f e l k h g i j m
13z+1/2,x+1/2,y
(
   0   0   1   1/2
   1   0   0   1/2
   0   1   0    0
)
 
d b a c e f l k h g i j m
14z+1/2,x,y+1/2
(
   0   0   1   1/2
   1   0   0    0
   0   1   0   1/2
)
 
b d c a e f l k g h j i m
15z,x+1/2,y+1/2
(
   0   0   1    0
   1   0   0   1/2
   0   1   0   1/2
)
 
c a b d e f k l h g j i m
16z+1/2,x+1/2,y+1/2
(
   0   0   1   1/2
   1   0   0   1/2
   0   1   0   1/2
)
 
a c d b f e k l g h i j m
17y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
 
a d c b e f i j g h k l m
18y+1/2,x,z
(
   0   1   0   1/2
   1   0   0    0
   0   0   1    0
)
 
d a b c f e i j h g l k m
19y,x+1/2,z
(
   0   1   0    0
   1   0   0   1/2
   0   0   1    0
)
 
b c d a f e j i g h l k m
20y,x,z+1/2
(
   0   1   0    0
   1   0   0    0
   0   0   1   1/2
)
 
c b a d f e j i h g k l m
21y+1/2,x+1/2,z
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1    0
)
 
c b a d e f j i h g k l m
22y+1/2,x,z+1/2
(
   0   1   0   1/2
   1   0   0    0
   0   0   1   1/2
)
 
b c d a e f j i g h l k m
23y,x+1/2,z+1/2
(
   0   1   0    0
   1   0   0   1/2
   0   0   1   1/2
)
 
d a b c e f i j h g l k m
24y+1/2,x+1/2,z+1/2
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1   1/2
)
 
a d c b f e i j g h k l m
25y,z,x
(
   0   1   0    0
   0   0   1    0
   1   0   0    0
)
 
a d b c e f i j k l g h m
26y+1/2,z,x
(
   0   1   0   1/2
   0   0   1    0
   1   0   0    0
)
 
d a c b f e i j l k h g m
27y,z+1/2,x
(
   0   1   0    0
   0   0   1   1/2
   1   0   0    0
)
 
c b d a f e j i k l h g m
28y,z,x+1/2
(
   0   1   0    0
   0   0   1    0
   1   0   0   1/2
)
 
b c a d f e j i l k g h m
29y+1/2,z+1/2,x
(
   0   1   0   1/2
   0   0   1   1/2
   1   0   0    0
)
 
b c a d e f j i l k g h m
30y+1/2,z,x+1/2
(
   0   1   0   1/2
   0   0   1    0
   1   0   0   1/2
)
 
c b d a e f j i k l h g m
31y,z+1/2,x+1/2
(
   0   1   0    0
   0   0   1   1/2
   1   0   0   1/2
)
 
d a c b e f i j l k h g m
32y+1/2,z+1/2,x+1/2
(
   0   1   0   1/2
   0   0   1   1/2
   1   0   0   1/2
)
 
a d b c f e i j k l g h m
33z,y,x
(
   0   0   1    0
   0   1   0    0
   1   0   0    0
)
 
a c b d e f k l i j g h m
34z+1/2,y,x
(
   0   0   1   1/2
   0   1   0    0
   1   0   0    0
)
 
c a d b f e k l j i h g m
35z,y+1/2,x
(
   0   0   1    0
   0   1   0   1/2
   1   0   0    0
)
 
d b c a f e l k i j h g m
36z,y,x+1/2
(
   0   0   1    0
   0   1   0    0
   1   0   0   1/2
)
 
b d a c f e l k j i g h m
37z+1/2,y+1/2,x
(
   0   0   1   1/2
   0   1   0   1/2
   1   0   0    0
)
 
b d a c e f l k j i g h m
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 e f l k i j h g m
39z,y+1/2,x+1/2
(
   0   0   1    0
   0   1   0   1/2
   1   0   0   1/2
)
 
c a d b e f k l j i h g m
40z+1/2,y+1/2,x+1/2
(
   0   0   1   1/2
   0   1   0   1/2
   1   0   0   1/2
)
 
a c b d f e k l i j g h m
41x,z,y
(
   1   0   0    0
   0   0   1    0
   0   1   0    0
)
 
a b d c e f g h k l i j m
42x+1/2,z,y
(
   1   0   0   1/2
   0   0   1    0
   0   1   0    0
)
 
b a c d f e g h l k j i m
43x,z+1/2,y
(
   1   0   0    0
   0   0   1   1/2
   0   1   0    0
)
 
c d b a f e h g k l j i m
44x,z,y+1/2
(
   1   0   0    0
   0   0   1    0
   0   1   0   1/2
)
 
d c a b f e h g l k i j m
45x+1/2,z+1/2,y
(
   1   0   0   1/2
   0   0   1   1/2
   0   1   0    0
)
 
d c a b e f h g l k i j m
46x+1/2,z,y+1/2
(
   1   0   0   1/2
   0   0   1    0
   0   1   0   1/2
)
 
c d b a e f h g k l j i m
47x,z+1/2,y+1/2
(
   1   0   0    0
   0   0   1   1/2
   0   1   0   1/2
)
 
b a c d e f g h l k j i m
48x+1/2,z+1/2,y+1/2
(
   1   0   0   1/2
   0   0   1   1/2
   0   1   0   1/2
)
 
a b d c f e g h k l i j m


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