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

Wyckoff Sets of Space Group P222 (No. 16)

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
u 4 1 (x, y, z) u u
t 2 ..2 (1/2 , 1/2 , z) qrst ijklmnopqrst
s 2 ..2 (0, 1/2 , z) qrst ijklmnopqrst
r 2 ..2 (1/2 , 0, z) qrst ijklmnopqrst
q 2 ..2 (0, 0, z) qrst ijklmnopqrst
p 2 .2. (1/2 , y, 1/2 ) mnop ijklmnopqrst
o 2 .2. (1/2 , y, 0) mnop ijklmnopqrst
n 2 .2. (0, y, 1/2 ) mnop ijklmnopqrst
m 2 .2. (0, y, 0) mnop ijklmnopqrst
l 2 2.. (x, 1/2 , 1/2 ) ijkl ijklmnopqrst
k 2 2.. (x, 1/2 , 0) ijkl ijklmnopqrst
j 2 2.. (x, 0, 1/2 ) ijkl ijklmnopqrst
i 2 2.. (x, 0, 0) ijkl ijklmnopqrst
h 1 222 (1/2 , 1/2 , 1/2 ) abcdefgh abcdefgh
g 1 222 (0, 1/2 , 1/2 ) abcdefgh abcdefgh
f 1 222 (1/2 , 0, 1/2 ) abcdefgh abcdefgh
e 1 222 (1/2 , 1/2 , 0) abcdefgh abcdefgh
d 1 222 (0, 0, 1/2 ) abcdefgh abcdefgh
c 1 222 (0, 1/2 , 0) abcdefgh abcdefgh
b 1 222 (1/2 , 0, 0) abcdefgh abcdefgh
a 1 222 (0, 0, 0) abcdefgh abcdefgh

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P222 (016) under the coset representatives of its affine normalizer


Index: 96

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
2x+1/2,y,z
(
   1   0   0   1/2
   0   1   0    0
   0   0   1    0
)
 
b a e f c d h g i j k l o p m n r q t s u
3x,y+1/2,z
(
   1   0   0    0
   0   1   0   1/2
   0   0   1    0
)
 
c e a g b h d f k l i j m n o p s t q r u
4x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
 
d f g a h b c e j i l k n m p o q r s t u
5x+1/2,y+1/2,z
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)
 
e c b h a g f d k l i j o p m n t s r q u
6x+1/2,y,z+1/2
(
   1   0   0   1/2
   0   1   0    0
   0   0   1   1/2
)
 
f d h b g a e c j i l k p o n m r q t s u
7x,y+1/2,z+1/2
(
   1   0   0    0
   0   1   0   1/2
   0   0   1   1/2
)
 
g h d c f e a b l k j i n m p o s t q r u
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 u
9-x,-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
10-x+1/2,-y,-z
(
  -1   0   0   1/2
   0  -1   0    0
   0   0  -1    0
)
 
b a e f c d h g i j k l o p m n r q t s u
11-x,-y+1/2,-z
(
  -1   0   0    0
   0  -1   0   1/2
   0   0  -1    0
)
 
c e a g b h d f k l i j m n o p s t q r u
12-x,-y,-z+1/2
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1   1/2
)
 
d f g a h b c e j i l k n m p o q r s t u
13-x+1/2,-y+1/2,-z
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1    0
)
 
e c b h a g f d k l i j o p m n t s r q u
14-x+1/2,-y,-z+1/2
(
  -1   0   0   1/2
   0  -1   0    0
   0   0  -1   1/2
)
 
f d h b g a e c j i l k p o n m r q t s u
15-x,-y+1/2,-z+1/2
(
  -1   0   0    0
   0  -1   0   1/2
   0   0  -1   1/2
)
 
g h d c f e a b l k j i n m p o s t q r u
16-x+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 u
17z,x,y
(
   0   0   1    0
   1   0   0    0
   0   1   0    0
)
 
a d b c f g e h q s r t i k j l m n o p u
18z+1/2,x,y
(
   0   0   1   1/2
   1   0   0    0
   0   1   0    0
)
 
d a f g b c h e q s r t j l i k n m p o u
19z,x+1/2,y
(
   0   0   1    0
   1   0   0   1/2
   0   1   0    0
)
 
b f a e d h c g r t q s i k j l o p m n u
20z,x,y+1/2
(
   0   0   1    0
   1   0   0    0
   0   1   0   1/2
)
 
c g e a h d b f s q t r k i l j m n o p u
21z+1/2,x+1/2,y
(
   0   0   1   1/2
   1   0   0   1/2
   0   1   0    0
)
 
f b d h a e g c r t q s j l i k p o n m u
22z+1/2,x,y+1/2
(
   0   0   1   1/2
   1   0   0    0
   0   1   0   1/2
)
 
g c h d e a f b s q t r l j k i n m p o u
23z,x+1/2,y+1/2
(
   0   0   1    0
   1   0   0   1/2
   0   1   0   1/2
)
 
e h c b g f a d t r s q k i l j o p m n u
24z+1/2,x+1/2,y+1/2
(
   0   0   1   1/2
   1   0   0   1/2
   0   1   0   1/2
)
 
h e g f c b d a t r s q l j k i p o n m u
25-z,-x,-y
(
   0   0  -1    0
  -1   0   0    0
   0  -1   0    0
)
 
a d b c f g e h q s r t i k j l m n o p u
26-z+1/2,-x,-y
(
   0   0  -1   1/2
  -1   0   0    0
   0  -1   0    0
)
 
d a f g b c h e q s r t j l i k n m p o u
27-z,-x+1/2,-y
(
   0   0  -1    0
  -1   0   0   1/2
   0  -1   0    0
)
 
b f a e d h c g r t q s i k j l o p m n u
28-z,-x,-y+1/2
(
   0   0  -1    0
  -1   0   0    0
   0  -1   0   1/2
)
 
c g e a h d b f s q t r k i l j m n o p u
29-z+1/2,-x+1/2,-y
(
   0   0  -1   1/2
  -1   0   0   1/2
   0  -1   0    0
)
 
f b d h a e g c r t q s j l i k p o n m u
30-z+1/2,-x,-y+1/2
(
   0   0  -1   1/2
  -1   0   0    0
   0  -1   0   1/2
)
 
g c h d e a f b s q t r l j k i n m p o u
31-z,-x+1/2,-y+1/2
(
   0   0  -1    0
  -1   0   0   1/2
   0  -1   0   1/2
)
 
e h c b g f a d t r s q k i l j o p m n u
32-z+1/2,-x+1/2,-y+1/2
(
   0   0  -1   1/2
  -1   0   0   1/2
   0  -1   0   1/2
)
 
h e g f c b d a t r s q l j k i p o n m u
33y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
 
a c b d e g f h m n o p i j k l q s r t u
34y+1/2,x,z
(
   0   1   0   1/2
   1   0   0    0
   0   0   1    0
)
 
c a e g b d h f m n o p k l i j s q t r u
35y,x+1/2,z
(
   0   1   0    0
   1   0   0   1/2
   0   0   1    0
)
 
b e a f c h d g o p m n i j k l r t q s u
36y,x,z+1/2
(
   0   1   0    0
   1   0   0    0
   0   0   1   1/2
)
 
d g f a h c b e n m p o j i l k q s r t u
37y+1/2,x+1/2,z
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1    0
)
 
e b c h a f g d o p m n k l i j t r s q u
38y+1/2,x,z+1/2
(
   0   1   0   1/2
   1   0   0    0
   0   0   1   1/2
)
 
g d h c f a e b n m p o l k j i s q t r u
39y,x+1/2,z+1/2
(
   0   1   0    0
   1   0   0   1/2
   0   0   1   1/2
)
 
f h d b g e a c p o n m j i l k r t q s u
40y+1/2,x+1/2,z+1/2
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1   1/2
)
 
h f g e d b c a p o n m l k j i t r s q u
41-y,-x,-z
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1    0
)
 
a c b d e g f h m n o p i j k l q s r t u
42-y+1/2,-x,-z
(
   0  -1   0   1/2
  -1   0   0    0
   0   0  -1    0
)
 
c a e g b d h f m n o p k l i j s q t r u
43-y,-x+1/2,-z
(
   0  -1   0    0
  -1   0   0   1/2
   0   0  -1    0
)
 
b e a f c h d g o p m n i j k l r t q s u
44-y,-x,-z+1/2
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1   1/2
)
 
d g f a h c b e n m p o j i l k q s r t u
45-y+1/2,-x+1/2,-z
(
   0  -1   0   1/2
  -1   0   0   1/2
   0   0  -1    0
)
 
e b c h a f g d o p m n k l i j t r s q u
46-y+1/2,-x,-z+1/2
(
   0  -1   0   1/2
  -1   0   0    0
   0   0  -1   1/2
)
 
g d h c f a e b n m p o l k j i s q t r u
47-y,-x+1/2,-z+1/2
(
   0  -1   0    0
  -1   0   0   1/2
   0   0  -1   1/2
)
 
f h d b g e a c p o n m j i l k r t q s u
48-y+1/2,-x+1/2,-z+1/2
(
   0  -1   0   1/2
  -1   0   0   1/2
   0   0  -1   1/2
)
 
h f g e d b c a p o n m l k j i t r s q u
49y,z,x
(
   0   1   0    0
   0   0   1    0
   1   0   0    0
)
 
a c d b g e f h m o n p q r s t i k j l u
50y+1/2,z,x
(
   0   1   0   1/2
   0   0   1    0
   1   0   0    0
)
 
c a g e d b h f m o n p s t q r k i l j u
51y,z+1/2,x
(
   0   1   0    0
   0   0   1   1/2
   1   0   0    0
)
 
d g a f c h b e n p m o q r s t j l i k u
52y,z,x+1/2
(
   0   1   0    0
   0   0   1    0
   1   0   0   1/2
)
 
b e f a h c d g o m p n r q t s i k j l u
53y+1/2,z+1/2,x
(
   0   1   0   1/2
   0   0   1   1/2
   1   0   0    0
)
 
g d c h a f e b n p m o s t q r l j k i u
54y+1/2,z,x+1/2
(
   0   1   0   1/2
   0   0   1    0
   1   0   0   1/2
)
 
e b h c f a g d o m p n t s r q k i l j u
55y,z+1/2,x+1/2
(
   0   1   0    0
   0   0   1   1/2
   1   0   0   1/2
)
 
f h b d e g a c p n o m r q t s j l i k u
56y+1/2,z+1/2,x+1/2
(
   0   1   0   1/2
   0   0   1   1/2
   1   0   0   1/2
)
 
h f e g b d c a p n o m t s r q l j k i u
57-y,-z,-x
(
   0  -1   0    0
   0   0  -1    0
  -1   0   0    0
)
 
a c d b g e f h m o n p q r s t i k j l u
58-y+1/2,-z,-x
(
   0  -1   0   1/2
   0   0  -1    0
  -1   0   0    0
)
 
c a g e d b h f m o n p s t q r k i l j u
59-y,-z+1/2,-x
(
   0  -1   0    0
   0   0  -1   1/2
  -1   0   0    0
)
 
d g a f c h b e n p m o q r s t j l i k u
60-y,-z,-x+1/2
(
   0  -1   0    0
   0   0  -1    0
  -1   0   0   1/2
)
 
b e f a h c d g o m p n r q t s i k j l u
61-y+1/2,-z+1/2,-x
(
   0  -1   0   1/2
   0   0  -1   1/2
  -1   0   0    0
)
 
g d c h a f e b n p m o s t q r l j k i u
62-y+1/2,-z,-x+1/2
(
   0  -1   0   1/2
   0   0  -1    0
  -1   0   0   1/2
)
 
e b h c f a g d o m p n t s r q k i l j u
63-y,-z+1/2,-x+1/2
(
   0  -1   0    0
   0   0  -1   1/2
  -1   0   0   1/2
)
 
f h b d e g a c p n o m r q t s j l i k u
64-y+1/2,-z+1/2,-x+1/2
(
   0  -1   0   1/2
   0   0  -1   1/2
  -1   0   0   1/2
)
 
h f e g b d c a p n o m t s r q l j k i u
65z,y,x
(
   0   0   1    0
   0   1   0    0
   1   0   0    0
)
 
a d c b g f e h q r s t m o n p i j k l u
66z+1/2,y,x
(
   0   0   1   1/2
   0   1   0    0
   1   0   0    0
)
 
d a g f c b h e q r s t n p m o j i l k u
67z,y+1/2,x
(
   0   0   1    0
   0   1   0   1/2
   1   0   0    0
)
 
c g a e d h b f s t q r m o n p k l i j u
68z,y,x+1/2
(
   0   0   1    0
   0   1   0    0
   1   0   0   1/2
)
 
b f e a h d c g r q t s o m p n i j k l u
69z+1/2,y+1/2,x
(
   0   0   1   1/2
   0   1   0   1/2
   1   0   0    0
)
 
g c d h a e f b s t q r n p m o l k j i u
70z+1/2,y,x+1/2
(
   0   0   1   1/2
   0   1   0    0
   1   0   0   1/2
)
 
f b h d e a g c r q t s p n o m j i l k u
71z,y+1/2,x+1/2
(
   0   0   1    0
   0   1   0   1/2
   1   0   0   1/2
)
 
e h b c f g a d t s r q o m p n k l i j u
72z+1/2,y+1/2,x+1/2
(
   0   0   1   1/2
   0   1   0   1/2
   1   0   0   1/2
)
 
h e f g b c d a t s r q p n o m l k j i u
73-z,-y,-x
(
   0   0  -1    0
   0  -1   0    0
  -1   0   0    0
)
 
a d c b g f e h q r s t m o n p i j k l u
74-z+1/2,-y,-x
(
   0   0  -1   1/2
   0  -1   0    0
  -1   0   0    0
)
 
d a g f c b h e q r s t n p m o j i l k u
75-z,-y+1/2,-x
(
   0   0  -1    0
   0  -1   0   1/2
  -1   0   0    0
)
 
c g a e d h b f s t q r m o n p k l i j u
76-z,-y,-x+1/2
(
   0   0  -1    0
   0  -1   0    0
  -1   0   0   1/2
)
 
b f e a h d c g r q t s o m p n i j k l u
77-z+1/2,-y+1/2,-x
(
   0   0  -1   1/2
   0  -1   0   1/2
  -1   0   0    0
)
 
g c d h a e f b s t q r n p m o l k j i u
78-z+1/2,-y,-x+1/2
(
   0   0  -1   1/2
   0  -1   0    0
  -1   0   0   1/2
)
 
f b h d e a g c r q t s p n o m j i l k u
79-z,-y+1/2,-x+1/2
(
   0   0  -1    0
   0  -1   0   1/2
  -1   0   0   1/2
)
 
e h b c f g a d t s r q o m p n k l i j u
80-z+1/2,-y+1/2,-x+1/2
(
   0   0  -1   1/2
   0  -1   0   1/2
  -1   0   0   1/2
)
 
h e f g b c d a t s r q p n o m l k j i u
81x,z,y
(
   1   0   0    0
   0   0   1    0
   0   1   0    0
)
 
a b d c f e g h i k j l q s r t m o n p u
82x+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 r t q s o m p n u
83x,z+1/2,y
(
   1   0   0    0
   0   0   1   1/2
   0   1   0    0
)
 
d f a g b h c e j l i k q s r t n p m o u
84x,z,y+1/2
(
   1   0   0    0
   0   0   1    0
   0   1   0   1/2
)
 
c e g a h b d f k i l j s q t r m o n p u
85x+1/2,z+1/2,y
(
   1   0   0   1/2
   0   0   1   1/2
   0   1   0    0
)
 
f d b h a g e c j l i k r t q s p n o m u
86x+1/2,z,y+1/2
(
   1   0   0   1/2
   0   0   1    0
   0   1   0   1/2
)
 
e c h b g a f d k i l j t r s q o m p n u
87x,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 s q t r n p m o u
88x+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 e f c d b a l j k i t r s q p n o m u
89-x,-z,-y
(
  -1   0   0    0
   0   0  -1    0
   0  -1   0    0
)
 
a b d c f e g h i k j l q s r t m o n p u
90-x+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 r t q s o m p n u
91-x,-z+1/2,-y
(
  -1   0   0    0
   0   0  -1   1/2
   0  -1   0    0
)
 
d f a g b h c e j l i k q s r t n p m o u
92-x,-z,-y+1/2
(
  -1   0   0    0
   0   0  -1    0
   0  -1   0   1/2
)
 
c e g a h b d f k i l j s q t r m o n p u
93-x+1/2,-z+1/2,-y
(
  -1   0   0   1/2
   0   0  -1   1/2
   0  -1   0    0
)
 
f d b h a g e c j l i k r t q s p n o m u
94-x+1/2,-z,-y+1/2
(
  -1   0   0   1/2
   0   0  -1    0
   0  -1   0   1/2
)
 
e c h b g a f d k i l j t r s q o m p n u
95-x,-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 s q t r n p m o u
96-x+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 e f c d b a l j k i t r s q p n o m u


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