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

Wyckoff Sets of Space Group P212121 (No. 19)

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
a 4 1 (x, y, z) a a

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P212121 (019) 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
2x+1/2,y,z
(
   1   0   0   1/2
   0   1   0    0
   0   0   1    0
)
 
a
3x,y+1/2,z
(
   1   0   0    0
   0   1   0   1/2
   0   0   1    0
)
 
a
4x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
 
a
5x+1/2,y+1/2,z
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)
 
a
6x+1/2,y,z+1/2
(
   1   0   0   1/2
   0   1   0    0
   0   0   1   1/2
)
 
a
7x,y+1/2,z+1/2
(
   1   0   0    0
   0   1   0   1/2
   0   0   1   1/2
)
 
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
)
 
a
9-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
 
a
10-x+1/2,-y,-z
(
  -1   0   0   1/2
   0  -1   0    0
   0   0  -1    0
)
 
a
11-x,-y+1/2,-z
(
  -1   0   0    0
   0  -1   0   1/2
   0   0  -1    0
)
 
a
12-x,-y,-z+1/2
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1   1/2
)
 
a
13-x+1/2,-y+1/2,-z
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1    0
)
 
a
14-x+1/2,-y,-z+1/2
(
  -1   0   0   1/2
   0  -1   0    0
   0   0  -1   1/2
)
 
a
15-x,-y+1/2,-z+1/2
(
  -1   0   0    0
   0  -1   0   1/2
   0   0  -1   1/2
)
 
a
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
)
 
a
17z,x,y
(
   0   0   1    0
   1   0   0    0
   0   1   0    0
)
 
a
18z+1/2,x,y
(
   0   0   1   1/2
   1   0   0    0
   0   1   0    0
)
 
a
19z,x+1/2,y
(
   0   0   1    0
   1   0   0   1/2
   0   1   0    0
)
 
a
20z,x,y+1/2
(
   0   0   1    0
   1   0   0    0
   0   1   0   1/2
)
 
a
21z+1/2,x+1/2,y
(
   0   0   1   1/2
   1   0   0   1/2
   0   1   0    0
)
 
a
22z+1/2,x,y+1/2
(
   0   0   1   1/2
   1   0   0    0
   0   1   0   1/2
)
 
a
23z,x+1/2,y+1/2
(
   0   0   1    0
   1   0   0   1/2
   0   1   0   1/2
)
 
a
24z+1/2,x+1/2,y+1/2
(
   0   0   1   1/2
   1   0   0   1/2
   0   1   0   1/2
)
 
a
25-z,-x,-y
(
   0   0  -1    0
  -1   0   0    0
   0  -1   0    0
)
 
a
26-z+1/2,-x,-y
(
   0   0  -1   1/2
  -1   0   0    0
   0  -1   0    0
)
 
a
27-z,-x+1/2,-y
(
   0   0  -1    0
  -1   0   0   1/2
   0  -1   0    0
)
 
a
28-z,-x,-y+1/2
(
   0   0  -1    0
  -1   0   0    0
   0  -1   0   1/2
)
 
a
29-z+1/2,-x+1/2,-y
(
   0   0  -1   1/2
  -1   0   0   1/2
   0  -1   0    0
)
 
a
30-z+1/2,-x,-y+1/2
(
   0   0  -1   1/2
  -1   0   0    0
   0  -1   0   1/2
)
 
a
31-z,-x+1/2,-y+1/2
(
   0   0  -1    0
  -1   0   0   1/2
   0  -1   0   1/2
)
 
a
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
)
 
a
33y+1/4,x+1/4,z+1/4
(
   0   1   0   1/4
   1   0   0   1/4
   0   0   1   1/4
)
 
a
34y+3/4,x+1/4,z+1/4
(
   0   1   0   3/4
   1   0   0   1/4
   0   0   1   1/4
)
 
a
35y+1/4,x+3/4,z+1/4
(
   0   1   0   1/4
   1   0   0   3/4
   0   0   1   1/4
)
 
a
36y+1/4,x+3/4,z+3/4
(
   0   1   0   1/4
   1   0   0   3/4
   0   0   1   3/4
)
 
a
37y+3/4,x+3/4,z+1/4
(
   0   1   0   3/4
   1   0   0   3/4
   0   0   1   1/4
)
 
a
38y+3/4,x+1/4,z+3/4
(
   0   1   0   3/4
   1   0   0   1/4
   0   0   1   3/4
)
 
a
39y+1/4,x+3/4,z+3/4
(
   0   1   0   1/4
   1   0   0   3/4
   0   0   1   3/4
)
 
a
40y+3/4,x+3/4,z+3/4
(
   0   1   0   3/4
   1   0   0   3/4
   0   0   1   3/4
)
 
a
41-y+1/4,-x+1/4,-z+1/4
(
   0  -1   0   1/4
  -1   0   0   1/4
   0   0  -1   1/4
)
 
a
42-y+3/4,-x+1/4,-z+1/4
(
   0  -1   0   3/4
  -1   0   0   1/4
   0   0  -1   1/4
)
 
a
43-y+1/4,-x+3/4,-z+1/4
(
   0  -1   0   1/4
  -1   0   0   3/4
   0   0  -1   1/4
)
 
a
44-y+1/4,-x+3/4,-z+3/4
(
   0  -1   0   1/4
  -1   0   0   3/4
   0   0  -1   3/4
)
 
a
45-y+3/4,-x+3/4,-z+1/4
(
   0  -1   0   3/4
  -1   0   0   3/4
   0   0  -1   1/4
)
 
a
46-y+3/4,-x+1/4,-z+3/4
(
   0  -1   0   3/4
  -1   0   0   1/4
   0   0  -1   3/4
)
 
a
47-y+1/4,-x+3/4,-z+3/4
(
   0  -1   0   1/4
  -1   0   0   3/4
   0   0  -1   3/4
)
 
a
48-y+3/4,-x+3/4,-z+3/4
(
   0  -1   0   3/4
  -1   0   0   3/4
   0   0  -1   3/4
)
 
a
49y,z,x
(
   0   1   0    0
   0   0   1    0
   1   0   0    0
)
 
a
50y+1/2,z,x
(
   0   1   0   1/2
   0   0   1    0
   1   0   0    0
)
 
a
51y,z+1/2,x
(
   0   1   0    0
   0   0   1   1/2
   1   0   0    0
)
 
a
52y,z,x+1/2
(
   0   1   0    0
   0   0   1    0
   1   0   0   1/2
)
 
a
53y+1/2,z+1/2,x
(
   0   1   0   1/2
   0   0   1   1/2
   1   0   0    0
)
 
a
54y+1/2,z,x+1/2
(
   0   1   0   1/2
   0   0   1    0
   1   0   0   1/2
)
 
a
55y,z+1/2,x+1/2
(
   0   1   0    0
   0   0   1   1/2
   1   0   0   1/2
)
 
a
56y+1/2,z+1/2,x+1/2
(
   0   1   0   1/2
   0   0   1   1/2
   1   0   0   1/2
)
 
a
57-y,-z,-x
(
   0  -1   0    0
   0   0  -1    0
  -1   0   0    0
)
 
a
58-y+1/2,-z,-x
(
   0  -1   0   1/2
   0   0  -1    0
  -1   0   0    0
)
 
a
59-y,-z+1/2,-x
(
   0  -1   0    0
   0   0  -1   1/2
  -1   0   0    0
)
 
a
60-y,-z,-x+1/2
(
   0  -1   0    0
   0   0  -1    0
  -1   0   0   1/2
)
 
a
61-y+1/2,-z+1/2,-x
(
   0  -1   0   1/2
   0   0  -1   1/2
  -1   0   0    0
)
 
a
62-y+1/2,-z,-x+1/2
(
   0  -1   0   1/2
   0   0  -1    0
  -1   0   0   1/2
)
 
a
63-y,-z+1/2,-x+1/2
(
   0  -1   0    0
   0   0  -1   1/2
  -1   0   0   1/2
)
 
a
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
)
 
a
65z+1/4,y+1/4,x+1/4
(
   0   0   1   1/4
   0   1   0   1/4
   1   0   0   1/4
)
 
a
66z+3/4,y+1/4,x+1/4
(
   0   0   1   3/4
   0   1   0   1/4
   1   0   0   1/4
)
 
a
67z+1/4,y+3/4,x+1/4
(
   0   0   1   1/4
   0   1   0   3/4
   1   0   0   1/4
)
 
a
68z+1/4,y+1/4,x+3/4
(
   0   0   1   1/4
   0   1   0   1/4
   1   0   0   3/4
)
 
a
69z+3/4,y+3/4,x+1/4
(
   0   0   1   3/4
   0   1   0   3/4
   1   0   0   1/4
)
 
a
70z+3/4,y+1/4,x+3/4
(
   0   0   1   3/4
   0   1   0   1/4
   1   0   0   3/4
)
 
a
71z+1/4,y+3/4,x+3/4
(
   0   0   1   1/4
   0   1   0   3/4
   1   0   0   3/4
)
 
a
72z+3/4,y+3/4,x+3/4
(
   0   0   1   3/4
   0   1   0   3/4
   1   0   0   3/4
)
 
a
73-z+1/4,-y+1/4,-x+1/4
(
   0   0  -1   1/4
   0  -1   0   1/4
  -1   0   0   1/4
)
 
a
74-z+3/4,-y+1/4,-x+1/4
(
   0   0  -1   3/4
   0  -1   0   1/4
  -1   0   0   1/4
)
 
a
75-z+1/4,-y+3/4,-x+1/4
(
   0   0  -1   1/4
   0  -1   0   3/4
  -1   0   0   1/4
)
 
a
76-z+1/4,-y+1/4,-x+3/4
(
   0   0  -1   1/4
   0  -1   0   1/4
  -1   0   0   3/4
)
 
a
77-z+3/4,-y+3/4,-x+1/4
(
   0   0  -1   3/4
   0  -1   0   3/4
  -1   0   0   1/4
)
 
a
78-z+3/4,-y+1/4,-x+3/4
(
   0   0  -1   3/4
   0  -1   0   1/4
  -1   0   0   3/4
)
 
a
79-z+1/4,-y+3/4,-x+3/4
(
   0   0  -1   1/4
   0  -1   0   3/4
  -1   0   0   3/4
)
 
a
80-z+3/4,-y+3/4,-x+3/4
(
   0   0  -1   3/4
   0  -1   0   3/4
  -1   0   0   3/4
)
 
a
81x+1/4,z+1/4,y+1/4
(
   1   0   0   1/4
   0   0   1   1/4
   0   1   0   1/4
)
 
a
82x+3/4,z+1/4,y+1/4
(
   1   0   0   3/4
   0   0   1   1/4
   0   1   0   1/4
)
 
a
83x+1/4,z+3/4,y+1/4
(
   1   0   0   1/4
   0   0   1   3/4
   0   1   0   1/4
)
 
a
84x+1/4,z+1/4,y+3/4
(
   1   0   0   1/4
   0   0   1   1/4
   0   1   0   3/4
)
 
a
85x+3/4,z+3/4,y+1/4
(
   1   0   0   3/4
   0   0   1   3/4
   0   1   0   1/4
)
 
a
86x+3/4,z+1/4,y+3/4
(
   1   0   0   3/4
   0   0   1   1/4
   0   1   0   3/4
)
 
a
87x+1/4,z+3/4,y+3/4
(
   1   0   0   1/4
   0   0   1   3/4
   0   1   0   3/4
)
 
a
88x+3/4,z+3/4,y+3/4
(
   1   0   0   3/4
   0   0   1   3/4
   0   1   0   3/4
)
 
a
89-x+1/4,-z+1/4,-y+1/4
(
  -1   0   0   1/4
   0   0  -1   1/4
   0  -1   0   1/4
)
 
a
90-x+3/4,-z+1/4,-y+1/4
(
  -1   0   0   3/4
   0   0  -1   1/4
   0  -1   0   1/4
)
 
a
91-x+1/4,-z+3/4,-y+1/4
(
  -1   0   0   1/4
   0   0  -1   3/4
   0  -1   0   1/4
)
 
a
92-x+1/4,-z+1/4,-y+3/4
(
  -1   0   0   1/4
   0   0  -1   1/4
   0  -1   0   3/4
)
 
a
93-x+3/4,-z+3/4,-y+1/4
(
  -1   0   0   3/4
   0   0  -1   3/4
   0  -1   0   1/4
)
 
a
94-x+3/4,-z+1/4,-y+3/4
(
  -1   0   0   3/4
   0   0  -1   1/4
   0  -1   0   3/4
)
 
a
95-x+1/4,-z+3/4,-y+3/4
(
  -1   0   0   1/4
   0   0  -1   3/4
   0  -1   0   3/4
)
 
a
96-x+3/4,-z+3/4,-y+3/4
(
  -1   0   0   3/4
   0   0  -1   3/4
   0  -1   0   3/4
)
 
a


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