Bilbao Crystallographic Server MGENPOS General Positions of Magnetic Space Groups Help

## General Positions of the Group Im-3m' (#229.143) 229.143 Im-3m' (UNI symbol)For this space group, BNS and OG settings coincide.Its label in the OG setting is given as: Im-3m' (#229.4.1641)

N Standard/Default Setting
(x,y,z) form Matrix form Geom. interp. Seitz notation
1 x, y, z, +1
mx,my,mz
 ``` 1 0 0 0 0 1 0 0 0 0 1 0```
1 +1 { 1 | 0 }
2 x, -y, -z, +1
mx,-my,-mz
 ``` 1 0 0 0 0 -1 0 0 0 0 -1 0```
2 x,0,0 +1 { 2100 | 0 }
3 -x, y, -z, +1
-mx,my,-mz
 ``` -1 0 0 0 0 1 0 0 0 0 -1 0```
2 0,y,0 +1 { 2010 | 0 }
4 -x, -y, z, +1
-mx,-my,mz
 ``` -1 0 0 0 0 -1 0 0 0 0 1 0```
2 0,0,z +1 { 2001 | 0 }
5 z, x, y, +1
mz,mx,my
 ``` 0 0 1 0 1 0 0 0 0 1 0 0```
3+ x,x,x +1 { 3+111 | 0 }
6 y, z, x, +1
my,mz,mx
 ``` 0 1 0 0 0 0 1 0 1 0 0 0```
3- x,x,x +1 { 3-111 | 0 }
7 -y, z, -x, +1
-my,mz,-mx
 ``` 0 -1 0 0 0 0 1 0 -1 0 0 0```
3- x,-x,-x +1 { 3-1-1-1 | 0 }
8 -z, -x, y, +1
-mz,-mx,my
 ``` 0 0 -1 0 -1 0 0 0 0 1 0 0```
3+ x,-x,-x +1 { 3+1-1-1 | 0 }
9 -y, -z, x, +1
-my,-mz,mx
 ``` 0 -1 0 0 0 0 -1 0 1 0 0 0```
3- -x,x,-x +1 { 3--11-1 | 0 }
10 z, -x, -y, +1
mz,-mx,-my
 ``` 0 0 1 0 -1 0 0 0 0 -1 0 0```
3+ -x,x,-x +1 { 3+-11-1 | 0 }
11 y, -z, -x, +1
my,-mz,-mx
 ``` 0 1 0 0 0 0 -1 0 -1 0 0 0```
3- -x,-x,x +1 { 3--1-11 | 0 }
12 -z, x, -y, +1
-mz,mx,-my
 ``` 0 0 -1 0 1 0 0 0 0 -1 0 0```
3+ -x,-x,x +1 { 3+-1-11 | 0 }
13 -x, -y, -z, +1
mx,my,mz
 ``` -1 0 0 0 0 -1 0 0 0 0 -1 0```
-1 0,0,0 +1 { -1 | 0 }
14 -x, y, z, +1
mx,-my,-mz
 ``` -1 0 0 0 0 1 0 0 0 0 1 0```
m 0,y,z +1 { m100 | 0 }
15 x, -y, z, +1
-mx,my,-mz
 ``` 1 0 0 0 0 -1 0 0 0 0 1 0```
m x,0,z +1 { m010 | 0 }
16 x, y, -z, +1
-mx,-my,mz
 ``` 1 0 0 0 0 1 0 0 0 0 -1 0```
m x,y,0 +1 { m001 | 0 }
17 -z, -x, -y, +1
mz,mx,my
 ``` 0 0 -1 0 -1 0 0 0 0 -1 0 0```
-3+ x,x,x 0,0,0 +1 { -3+111 | 0 }
18 -y, -z, -x, +1
my,mz,mx
 ``` 0 -1 0 0 0 0 -1 0 -1 0 0 0```
-3- x,x,x 0,0,0 +1 { -3-111 | 0 }
19 y, -z, x, +1
-my,mz,-mx
 ``` 0 1 0 0 0 0 -1 0 1 0 0 0```
-3- x,-x,-x 0,0,0 +1 { -3-1-1-1 | 0 }
20 z, x, -y, +1
-mz,-mx,my
 ``` 0 0 1 0 1 0 0 0 0 -1 0 0```
-3+ x,-x,-x 0,0,0 +1 { -3+1-1-1 | 0 }
21 y, z, -x, +1
-my,-mz,mx
 ``` 0 1 0 0 0 0 1 0 -1 0 0 0```
-3- -x,x,-x 0,0,0 +1 { -3--11-1 | 0 }
22 -z, x, y, +1
mz,-mx,-my
 ``` 0 0 -1 0 1 0 0 0 0 1 0 0```
-3+ -x,x,-x 0,0,0 +1 { -3+-11-1 | 0 }
23 -y, z, x, +1
my,-mz,-mx
 ``` 0 -1 0 0 0 0 1 0 1 0 0 0```
-3- -x,-x,x 0,0,0 +1 { -3--1-11 | 0 }
24 z, -x, y, +1
-mz,mx,-my
 ``` 0 0 1 0 -1 0 0 0 0 1 0 0```
-3+ -x,-x,x 0,0,0 +1 { -3+-1-11 | 0 }
25 x, -z, y, -1
-mx,mz,-my
 ``` 1 0 0 0 0 0 -1 0 0 1 0 0``` '
4+ x,0,0 -1 { 4'+100 | 0 }
26 x, z, -y, -1
-mx,-mz,my
 ``` 1 0 0 0 0 0 1 0 0 -1 0 0``` '
4- x,0,0 -1 { 4'-100 | 0 }
27 z, y, -x, -1
-mz,-my,mx
 ``` 0 0 1 0 0 1 0 0 -1 0 0 0``` '
4+ 0,y,0 -1 { 4'+010 | 0 }
28 -z, y, x, -1
mz,-my,-mx
 ``` 0 0 -1 0 0 1 0 0 1 0 0 0``` '
4- 0,y,0 -1 { 4'-010 | 0 }
29 -y, x, z, -1
my,-mx,-mz
 ``` 0 -1 0 0 1 0 0 0 0 0 1 0``` '
4+ 0,0,z -1 { 4'+001 | 0 }
30 y, -x, z, -1
-my,mx,-mz
 ``` 0 1 0 0 -1 0 0 0 0 0 1 0``` '
4- 0,0,z -1 { 4'-001 | 0 }
31 y, x, -z, -1
-my,-mx,mz
 ``` 0 1 0 0 1 0 0 0 0 0 -1 0``` '
2 x,x,0 -1 { 2'110 | 0 }
32 -y, -x, -z, -1
my,mx,mz
 ``` 0 -1 0 0 -1 0 0 0 0 0 -1 0``` '
2 x,-x,0 -1 { 2'1-10 | 0 }
33 -x, z, y, -1
mx,-mz,-my
 ``` -1 0 0 0 0 0 1 0 0 1 0 0``` '
2 0,y,y -1 { 2'011 | 0 }
34 -x, -z, -y, -1
mx,mz,my
 ``` -1 0 0 0 0 0 -1 0 0 -1 0 0``` '
2 0,y,-y -1 { 2'01-1 | 0 }
35 z, -y, x, -1
-mz,my,-mx
 ``` 0 0 1 0 0 -1 0 0 1 0 0 0``` '
2 x,0,x -1 { 2'101 | 0 }
36 -z, -y, -x, -1
mz,my,mx
 ``` 0 0 -1 0 0 -1 0 0 -1 0 0 0``` '
2 -x,0,x -1 { 2'-101 | 0 }
37 -x, z, -y, -1
-mx,mz,-my
 ``` -1 0 0 0 0 0 1 0 0 -1 0 0``` '
-4+ x,0,0 0,0,0 -1 { -4'+100 | 0 }
38 -x, -z, y, -1
-mx,-mz,my
 ``` -1 0 0 0 0 0 -1 0 0 1 0 0``` '
-4- x,0,0 0,0,0 -1 { -4'-100 | 0 }
39 -z, -y, x, -1
-mz,-my,mx
 ``` 0 0 -1 0 0 -1 0 0 1 0 0 0``` '
-4+ 0,y,0 0,0,0 -1 { -4'+010 | 0 }
40 z, -y, -x, -1
mz,-my,-mx
 ``` 0 0 1 0 0 -1 0 0 -1 0 0 0``` '
-4- 0,y,0 0,0,0 -1 { -4'-010 | 0 }
41 y, -x, -z, -1
my,-mx,-mz
 ``` 0 1 0 0 -1 0 0 0 0 0 -1 0``` '
-4+ 0,0,z 0,0,0 -1 { -4'+001 | 0 }
42 -y, x, -z, -1
-my,mx,-mz
 ``` 0 -1 0 0 1 0 0 0 0 0 -1 0``` '
-4- 0,0,z 0,0,0 -1 { -4'-001 | 0 }
43 -y, -x, z, -1
-my,-mx,mz
 ``` 0 -1 0 0 -1 0 0 0 0 0 1 0``` '
m x,-x,z -1 { m'110 | 0 }
44 y, x, z, -1
my,mx,mz
 ``` 0 1 0 0 1 0 0 0 0 0 1 0``` '
m x,x,z -1 { m'1-10 | 0 }
45 x, -z, -y, -1
mx,-mz,-my
 ``` 1 0 0 0 0 0 -1 0 0 -1 0 0``` '
m x,y,-y -1 { m'011 | 0 }
46 x, z, y, -1
mx,mz,my
 ``` 1 0 0 0 0 0 1 0 0 1 0 0``` '
m x,y,y -1 { m'01-1 | 0 }
47 -z, y, -x, -1
-mz,my,-mx
 ``` 0 0 -1 0 0 1 0 0 -1 0 0 0``` '
m -x,y,x -1 { m'101 | 0 }
48 z, y, x, -1
mz,my,mx
 ``` 0 0 1 0 0 1 0 0 1 0 0 0``` '
m x,y,x -1 { m'-101 | 0 }
49 x+1/2, y+1/2, z+1/2, +1
mx,my,mz
 ``` 1 0 0 1/2 0 1 0 1/2 0 0 1 1/2```
t (1/2,1/2,1/2) +1 { 1 | 1/2 1/2 1/2 }
50 x+1/2, -y+1/2, -z+1/2, +1
mx,-my,-mz
 ``` 1 0 0 1/2 0 -1 0 1/2 0 0 -1 1/2```
2 (1/2,0,0) x,1/4,1/4 +1 { 2100 | 1/2 1/2 1/2 }
51 -x+1/2, y+1/2, -z+1/2, +1
-mx,my,-mz
 ``` -1 0 0 1/2 0 1 0 1/2 0 0 -1 1/2```
2 (0,1/2,0) 1/4,y,1/4 +1 { 2010 | 1/2 1/2 1/2 }
52 -x+1/2, -y+1/2, z+1/2, +1
-mx,-my,mz
 ``` -1 0 0 1/2 0 -1 0 1/2 0 0 1 1/2```
2 (0,0,1/2) 1/4,1/4,z +1 { 2001 | 1/2 1/2 1/2 }
53 z+1/2, x+1/2, y+1/2, +1
mz,mx,my
 ``` 0 0 1 1/2 1 0 0 1/2 0 1 0 1/2```
3+ (1/2,1/2,1/2) x,x,x +1 { 3+111 | 1/2 1/2 1/2 }
54 y+1/2, z+1/2, x+1/2, +1
my,mz,mx
 ``` 0 1 0 1/2 0 0 1 1/2 1 0 0 1/2```
3- (1/2,1/2,1/2) x,x,x +1 { 3-111 | 1/2 1/2 1/2 }
55 -y+1/2, z+1/2, -x+1/2, +1
-my,mz,-mx
 ``` 0 -1 0 1/2 0 0 1 1/2 -1 0 0 1/2```
3- (-1/6,1/6,1/6) x+1/3,-x+1/3,-x +1 { 3-1-1-1 | 1/2 1/2 1/2 }
56 -z+1/2, -x+1/2, y+1/2, +1
-mz,-mx,my
 ``` 0 0 -1 1/2 -1 0 0 1/2 0 1 0 1/2```
3+ (-1/6,1/6,1/6) x+2/3,-x,-x +1 { 3+1-1-1 | 1/2 1/2 1/2 }
57 -y+1/2, -z+1/2, x+1/2, +1
-my,-mz,mx
 ``` 0 -1 0 1/2 0 0 -1 1/2 1 0 0 1/2```
3- (1/6,-1/6,1/6) -x-1/3,x+2/3,-x +1 { 3--11-1 | 1/2 1/2 1/2 }
58 z+1/2, -x+1/2, -y+1/2, +1
mz,-mx,-my
 ``` 0 0 1 1/2 -1 0 0 1/2 0 -1 0 1/2```
3+ (1/6,-1/6,1/6) -x+1/3,x+1/3,-x +1 { 3+-11-1 | 1/2 1/2 1/2 }
59 y+1/2, -z+1/2, -x+1/2, +1
my,-mz,-mx
 ``` 0 1 0 1/2 0 0 -1 1/2 -1 0 0 1/2```
3- (1/6,1/6,-1/6) -x+2/3,-x+1/3,x +1 { 3--1-11 | 1/2 1/2 1/2 }
60 -z+1/2, x+1/2, -y+1/2, +1
-mz,mx,-my
 ``` 0 0 -1 1/2 1 0 0 1/2 0 -1 0 1/2```
3+ (1/6,1/6,-1/6) -x+1/3,-x+2/3,x +1 { 3+-1-11 | 1/2 1/2 1/2 }
61 -x+1/2, -y+1/2, -z+1/2, +1
mx, my, mz
 ``` -1 0 0 1/2 0 -1 0 1/2 0 0 -1 1/2```
-1 1/4,1/4,1/4 +1 { -1 | 1/2 1/2 1/2 }
62 -x+1/2, y+1/2, z+1/2, +1
mx, -my, -mz
 ``` -1 0 0 1/2 0 1 0 1/2 0 0 1 1/2```
n (0,1/2,1/2) 1/4,y,z +1 { m100 | 1/2 1/2 1/2 }
63 x+1/2, -y+1/2, z+1/2, +1
-mx, my, -mz
 ``` 1 0 0 1/2 0 -1 0 1/2 0 0 1 1/2```
n (1/2,0,1/2) x,1/4,z +1 { m010 | 1/2 1/2 1/2 }
64 x+1/2, y+1/2, -z+1/2, +1
-mx, -my, mz
 ``` 1 0 0 1/2 0 1 0 1/2 0 0 -1 1/2```
n (1/2,1/2,0) x,y,1/4 +1 { m001 | 1/2 1/2 1/2 }
65 -z+1/2, -x+1/2, -y+1/2, +1
mz, mx, my
 ``` 0 0 -1 1/2 -1 0 0 1/2 0 -1 0 1/2```
-3+ x,x,x 1/4,1/4,1/4 +1 { -3+111 | 1/2 1/2 1/2 }
66 -y+1/2, -z+1/2, -x+1/2, +1
my, mz, mx
 ``` 0 -1 0 1/2 0 0 -1 1/2 -1 0 0 1/2```
-3- x,x,x 1/4,1/4,1/4 +1 { -3-111 | 1/2 1/2 1/2 }
67 y+1/2, -z+1/2, x+1/2, +1
-my, mz, -mx
 ``` 0 1 0 1/2 0 0 -1 1/2 1 0 0 1/2```
-3- x+1,-x,-x 1/4,-1/4,3/4 +1 { -3-1-1-1 | 1/2 1/2 1/2 }
68 z+1/2, x+1/2, -y+1/2, +1
-mz, -mx, my
 ``` 0 0 1 1/2 1 0 0 1/2 0 -1 0 1/2```
-3+ x,-x+1,-x 1/4,3/4,-1/4 +1 { -3+1-1-1 | 1/2 1/2 1/2 }
69 y+1/2, z+1/2, -x+1/2, +1
-my, -mz, mx
 ``` 0 1 0 1/2 0 0 1 1/2 -1 0 0 1/2```
-3- -x+1,x,-x 3/4,1/4,-1/4 +1 { -3--11-1 | 1/2 1/2 1/2 }
70 -z+1/2, x+1/2, y+1/2, +1
mz, -mx, -my
 ``` 0 0 -1 1/2 1 0 0 1/2 0 1 0 1/2```
-3+ -x-1,x+1,-x -1/4,1/4,3/4 +1 { -3+-11-1 | 1/2 1/2 1/2 }
71 -y+1/2, z+1/2, x+1/2, +1
my, -mz, -mx
 ``` 0 -1 0 1/2 0 0 1 1/2 1 0 0 1/2```
-3- -x,-x+1,x -1/4,3/4,1/4 +1 { -3--1-11 | 1/2 1/2 1/2 }
72 z+1/2, -x+1/2, y+1/2, +1
-mz, mx, -my
 ``` 0 0 1 1/2 -1 0 0 1/2 0 1 0 1/2```
-3+ -x+1,-x,x 3/4,-1/4,1/4 +1 { -3+-1-11 | 1/2 1/2 1/2 }
73 x+1/2, -z+1/2, y+1/2, -1
-mx, mz, -my
 ``` 1 0 0 1/2 0 0 -1 1/2 0 1 0 1/2``` '
4+ (1/2,0,0) x,0,1/2 -1 { 4'+100 | 1/2 1/2 1/2 }
74 x+1/2, z+1/2, -y+1/2, -1
-mx, -mz, my
 ``` 1 0 0 1/2 0 0 1 1/2 0 -1 0 1/2``` '
4- (1/2,0,0) x,1/2,0 -1 { 4'-100 | 1/2 1/2 1/2 }
75 z+1/2, y+1/2, -x+1/2, -1
-mz, -my, mx
 ``` 0 0 1 1/2 0 1 0 1/2 -1 0 0 1/2``` '
4+ (0,1/2,0) 1/2,y,0 -1 { 4'+010 | 1/2 1/2 1/2 }
76 -z+1/2, y+1/2, x+1/2, -1
mz, -my, -mx
 ``` 0 0 -1 1/2 0 1 0 1/2 1 0 0 1/2``` '
4- (0,1/2,0) 0,y,1/2 -1 { 4'-010 | 1/2 1/2 1/2 }
77 -y+1/2, x+1/2, z+1/2, -1
my, -mx, -mz
 ``` 0 -1 0 1/2 1 0 0 1/2 0 0 1 1/2``` '
4+ (0,0,1/2) 0,1/2,z -1 { 4'+001 | 1/2 1/2 1/2 }
78 y+1/2, -x+1/2, z+1/2, -1
-my, mx, -mz
 ``` 0 1 0 1/2 -1 0 0 1/2 0 0 1 1/2``` '
4- (0,0,1/2) 1/2,0,z -1 { 4'-001 | 1/2 1/2 1/2 }
79 y+1/2, x+1/2, -z+1/2, -1
-my, -mx, mz
 ``` 0 1 0 1/2 1 0 0 1/2 0 0 -1 1/2``` '
2 (1/2,1/2,0) x,x,1/4 -1 { 2'110 | 1/2 1/2 1/2 }
80 -y+1/2, -x+1/2, -z+1/2, -1
my, mx, mz
 ``` 0 -1 0 1/2 -1 0 0 1/2 0 0 -1 1/2``` '
2 x,-x+1/2,1/4 -1 { 2'1-10 | 1/2 1/2 1/2 }
81 -x+1/2, z+1/2, y+1/2, -1
mx, -mz, -my
 ``` -1 0 0 1/2 0 0 1 1/2 0 1 0 1/2``` '
2 (0,1/2,1/2) 1/4,y,y -1 { 2'011 | 1/2 1/2 1/2 }
82 -x+1/2, -z+1/2, -y+1/2, -1
mx, mz, my
 ``` -1 0 0 1/2 0 0 -1 1/2 0 -1 0 1/2``` '
2 1/4,y+1/2,-y -1 { 2'01-1 | 1/2 1/2 1/2 }
83 z+1/2, -y+1/2, x+1/2, -1
-mz, my, -mx
 ``` 0 0 1 1/2 0 -1 0 1/2 1 0 0 1/2``` '
2 (1/2,0,1/2) x,1/4,x -1 { 2'101 | 1/2 1/2 1/2 }
84 -z+1/2, -y+1/2, -x+1/2, -1
mz, my, mx
 ``` 0 0 -1 1/2 0 -1 0 1/2 -1 0 0 1/2``` '
2 -x+1/2,1/4,x -1 { 2'-101 | 1/2 1/2 1/2 }
85 -x+1/2, z+1/2, -y+1/2, -1
-mx,mz,-my
 ``` -1 0 0 1/2 0 0 1 1/2 0 -1 0 1/2``` '
-4+ x,1/2,0 1/4,1/2,0 -1 { -4'+100 | 1/2 1/2 1/2 }
86 -x+1/2, -z+1/2, y+1/2, -1
-mx,-mz,my
 ``` -1 0 0 1/2 0 0 -1 1/2 0 1 0 1/2``` '
-4- x,0,1/2 1/4,0,1/2 -1 { -4'-100 | 1/2 1/2 1/2 }
87 -z+1/2, -y+1/2, x+1/2, -1
-mz,-my,mx
 ``` 0 0 -1 1/2 0 -1 0 1/2 1 0 0 1/2``` '
-4+ 0,y,1/2 0,1/4,1/2 -1 { -4'+010 | 1/2 1/2 1/2 }
88 z+1/2, -y+1/2, -x+1/2, -1
mz,-my,-mx
 ``` 0 0 1 1/2 0 -1 0 1/2 -1 0 0 1/2``` '
-4- 1/2,y,0 1/2,1/4,0 -1 { -4'-010 | 1/2 1/2 1/2 }
89 y+1/2, -x+1/2, -z+1/2, -1
my,-mx,-mz
 ``` 0 1 0 1/2 -1 0 0 1/2 0 0 -1 1/2``` '
-4+ 1/2,0,z 1/2,0,1/4 -1 { -4'+001 | 1/2 1/2 1/2 }
90 -y+1/2, x+1/2, -z+1/2, -1
-my,mx,-mz
 ``` 0 -1 0 1/2 1 0 0 1/2 0 0 -1 1/2``` '
-4- 0,1/2,z 0,1/2,1/4 -1 { -4'-001 | 1/2 1/2 1/2 }
91 -y+1/2, -x+1/2, z+1/2, -1
-my,-mx,mz
 ``` 0 -1 0 1/2 -1 0 0 1/2 0 0 1 1/2``` '
c x+1/2,-x,z -1 { m'110 | 1/2 1/2 1/2 }
92 y+1/2, x+1/2, z+1/2, -1
my,mx,mz
 ``` 0 1 0 1/2 1 0 0 1/2 0 0 1 1/2``` '
n (1/2,1/2,1/2) x,x,z -1 { m'1-10 | 1/2 1/2 1/2 }
93 x+1/2, -z+1/2, -y+1/2, -1
mx,-mz,-my
 ``` 1 0 0 1/2 0 0 -1 1/2 0 -1 0 1/2``` '
a x,y+1/2,-y -1 { m'011 | 1/2 1/2 1/2 }
94 x+1/2, z+1/2, y+1/2, -1
mx,mz,my
 ``` 1 0 0 1/2 0 0 1 1/2 0 1 0 1/2``` '
n (1/2,1/2,1/2) x,y,y -1 { m'01-1 | 1/2 1/2 1/2 }
95 -z+1/2, y+1/2, -x+1/2, -1
-mz,my,-mx
 ``` 0 0 -1 1/2 0 1 0 1/2 -1 0 0 1/2``` '
b -x+1/2,y,x -1 { m'101 | 1/2 1/2 1/2 }
96 z+1/2, y+1/2, x+1/2, -1
mz,my,mx
 ``` 0 0 1 1/2 0 1 0 1/2 1 0 0 1/2``` '
n (1/2,1/2,1/2) x,y,x -1 { m'-101 | 1/2 1/2 1/2 }

Go to the list of the Wyckoff Positions of the Group Im-3m' (#229.143)
Go to the Systematic Absences for the Group Im-3m' (#229.143)

 Bilbao Crystallographic Serverhttp://www.cryst.ehu.es