Bilbao Crystallographic Server MGENPOS General Positions of Magnetic Space Groups Help

## General Positions of the Group Ia-3 (#206.37) 206.37 Ia-3.1 (UNI symbol)For this space group, BNS and OG settings coincide.Its label in the OG setting is given as: Ia-3 (#206.1.1538)

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+1/2, +1
mx,-my,-mz
 ``` 1 0 0 0 0 -1 0 0 0 0 -1 1/2```
2 x,0,1/4 +1 { 2100 | 0 0 1/2 }
3 -x+1/2, y, -z, +1
-mx,my,-mz
 ``` -1 0 0 1/2 0 1 0 0 0 0 -1 0```
2 1/4,y,0 +1 { 2010 | 1/2 0 0 }
4 -x, -y+1/2, z, +1
-mx,-my,mz
 ``` -1 0 0 0 0 -1 0 1/2 0 0 1 0```
2 0,1/4,z +1 { 2001 | 0 1/2 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+1/2, z, -x, +1
-my,mz,-mx
 ``` 0 -1 0 1/2 0 0 1 0 -1 0 0 0```
3- (1/6,-1/6,-1/6) x+1/6,-x+1/6,-x +1 { 3-1-1-1 | 1/2 0 0 }
8 -z, -x+1/2, y, +1
-mz,-mx,my
 ``` 0 0 -1 0 -1 0 0 1/2 0 1 0 0```
3+ (-1/6,1/6,1/6) x+1/6,-x+1/6,-x +1 { 3+1-1-1 | 0 1/2 0 }
9 -y, -z+1/2, x, +1
-my,-mz,mx
 ``` 0 -1 0 0 0 0 -1 1/2 1 0 0 0```
3- (-1/6,1/6,-1/6) -x-1/6,x+1/3,-x +1 { 3--11-1 | 0 1/2 0 }
10 z, -x, -y+1/2, +1
mz,-mx,-my
 ``` 0 0 1 0 -1 0 0 0 0 -1 0 1/2```
3+ (1/6,-1/6,1/6) -x-1/6,x+1/3,-x +1 { 3+-11-1 | 0 0 1/2 }
11 y, -z, -x+1/2, +1
my,-mz,-mx
 ``` 0 1 0 0 0 0 -1 0 -1 0 0 1/2```
3- (-1/6,-1/6,1/6) -x+1/3,-x+1/6,x +1 { 3--1-11 | 0 0 1/2 }
12 -z+1/2, x, -y, +1
-mz,mx,-my
 ``` 0 0 -1 1/2 1 0 0 0 0 -1 0 0```
3+ (1/6,1/6,-1/6) -x+1/3,-x+1/6,x +1 { 3+-1-11 | 1/2 0 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+1/2, +1
mx,-my,-mz
 ``` -1 0 0 0 0 1 0 0 0 0 1 1/2```
c 0,y,z +1 { m100 | 0 0 1/2 }
15 x+1/2, -y, z, +1
-mx,my,-mz
 ``` 1 0 0 1/2 0 -1 0 0 0 0 1 0```
a x,0,z +1 { m010 | 1/2 0 0 }
16 x, y+1/2, -z, +1
-mx,-my,mz
 ``` 1 0 0 0 0 1 0 1/2 0 0 -1 0```
b x,y,0 +1 { m001 | 0 1/2 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+1/2, -z, x, +1
-my,mz,-mx
 ``` 0 1 0 1/2 0 0 -1 0 1 0 0 0```
-3- x+1/2,-x,-x 1/4,-1/4,1/4 +1 { -3-1-1-1 | 1/2 0 0 }
20 z, x+1/2, -y, +1
-mz,-mx,my
 ``` 0 0 1 0 1 0 0 1/2 0 -1 0 0```
-3+ x-0.5,-x+1/2,-x -1/4,1/4,-1/4 +1 { -3+1-1-1 | 0 1/2 0 }
21 y, z+1/2, -x, +1
-my,-mz,mx
 ``` 0 1 0 0 0 0 1 1/2 -1 0 0 0```
-3- -x+1/2,x,-x 1/4,1/4,-1/4 +1 { -3--11-1 | 0 1/2 0 }
22 -z, x, y+1/2, +1
mz,-mx,-my
 ``` 0 0 -1 0 1 0 0 0 0 1 0 1/2```
-3+ -x-1/2,x,-x -1/4,-1/4,1/4 +1 { -3+-11-1 | 0 0 1/2 }
23 -y, z, x+1/2, +1
my,-mz,-mx
 ``` 0 -1 0 0 0 0 1 0 1 0 0 1/2```
-3- -x,-x+1/2,x -1/4,1/4,1/4 +1 { -3--1-11 | 0 0 1/2 }
24 z+1/2, -x, y, +1
-mz,mx,-my
 ``` 0 0 1 1/2 -1 0 0 0 0 1 0 0```
-3+ -x,-x,x 1/4,-1/4,-1/4 +1 { -3+-1-11 | 1/2 0 0 }
25 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 }
26 x+1/2, -y+1/2, -z, +1
mx,-my,-mz
 ``` 1 0 0 1/2 0 -1 0 1/2 0 0 -1 0```
2 (1/2,0,0) x,1/4,0 +1 { 2100 | 1/2 1/2 0 }
27 -x, y+1/2, -z+1/2, +1
-mx,my,-mz
 ``` -1 0 0 0 0 1 0 1/2 0 0 -1 1/2```
2 (0,1/2,0) 0,y,1/4 +1 { 2010 | 0 1/2 1/2 }
28 -x+1/2, -y, z+1/2, +1
-mx,-my,mz
 ``` -1 0 0 1/2 0 -1 0 0 0 0 1 1/2```
2 (0,0,1/2) 1/4,0,z +1 { 2001 | 1/2 0 1/2 }
29 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 }
30 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 }
31 -y, z+1/2, -x+1/2, +1
-my,mz,-mx
 ``` 0 -1 0 0 0 0 1 1/2 -1 0 0 1/2```
3- (-1/3,1/3,1/3) x+1/6,-x+1/6,-x +1 { 3-1-1-1 | 0 1/2 1/2 }
32 -z+1/2, -x, y+1/2, +1
-mz,-mx,my
 ``` 0 0 -1 1/2 -1 0 0 0 0 1 0 1/2```
3+ x+1/2,-x,-x +1 { 3+1-1-1 | 1/2 0 1/2 }
33 -y+1/2, -z, x+1/2, +1
-my,-mz,mx
 ``` 0 -1 0 1/2 0 0 -1 0 1 0 0 1/2```
3- (1/3,-1/3,1/3) -x-1/6,x+1/3,-x +1 { 3--11-1 | 1/2 0 1/2 }
34 z+1/2, -x+1/2, -y, +1
mz,-mx,-my
 ``` 0 0 1 1/2 -1 0 0 1/2 0 -1 0 0```
3+ -x+1/2,x,-x +1 { 3+-11-1 | 1/2 1/2 0 }
35 y+1/2, -z+1/2, -x, +1
my,-mz,-mx
 ``` 0 1 0 1/2 0 0 -1 1/2 -1 0 0 0```
3- (1/3,1/3,-1/3) -x+1/3,-x+1/6,x +1 { 3--1-11 | 1/2 1/2 0 }
36 -z, x+1/2, -y+1/2, +1
-mz,mx,-my
 ``` 0 0 -1 0 1 0 0 1/2 0 -1 0 1/2```
3+ -x,-x+1/2,x +1 { 3+-1-11 | 0 1/2 1/2 }
37 -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 }
38 -x+1/2, y+1/2, z, +1
mx, -my, -mz
 ``` -1 0 0 1/2 0 1 0 1/2 0 0 1 0```
b 1/4,y,z +1 { m100 | 1/2 1/2 0 }
39 x, -y+1/2, z+1/2, +1
-mx, my, -mz
 ``` 1 0 0 0 0 -1 0 1/2 0 0 1 1/2```
c x,1/4,z +1 { m010 | 0 1/2 1/2 }
40 x+1/2, y, -z+1/2, +1
-mx, -my, mz
 ``` 1 0 0 1/2 0 1 0 0 0 0 -1 1/2```
a x,y,1/4 +1 { m001 | 1/2 0 1/2 }
41 -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 }
42 -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 }
43 y, -z+1/2, x+1/2, +1
-my, mz, -mx
 ``` 0 1 0 0 0 0 -1 1/2 1 0 0 1/2```
-3- x+1/2,-x,-x 0,0,1/2 +1 { -3-1-1-1 | 0 1/2 1/2 }
44 z+1/2, x, -y+1/2, +1
-mz, -mx, my
 ``` 0 0 1 1/2 1 0 0 0 0 -1 0 1/2```
-3+ x+1/2,-x+1/2,-x 1/2,1/2,0 +1 { -3+1-1-1 | 1/2 0 1/2 }
45 y+1/2, z, -x+1/2, +1
-my, -mz, mx
 ``` 0 1 0 1/2 0 0 1 0 -1 0 0 1/2```
-3- -x+1/2,x,-x 1/2,0,0 +1 { -3--11-1 | 1/2 0 1/2 }
46 -z+1/2, x+1/2, y, +1
mz, -mx, -my
 ``` 0 0 -1 1/2 1 0 0 1/2 0 1 0 0```
-3+ -x-1/2,x+1,-x 0,1/2,1/2 +1 { -3+-11-1 | 1/2 1/2 0 }
47 -y+1/2, z+1/2, x, +1
my, -mz, -mx
 ``` 0 -1 0 1/2 0 0 1 1/2 1 0 0 0```
-3- -x,-x+1/2,x 0,1/2,0 +1 { -3--1-11 | 1/2 1/2 0 }
48 z, -x+1/2, y+1/2, +1
-mz, mx, -my
 ``` 0 0 1 0 -1 0 0 1/2 0 1 0 1/2```
-3+ -x+1,-x+1/2,x 1/2,0,1/2 +1 { -3+-1-11 | 0 1/2 1/2 }

Go to the list of the Wyckoff Positions of the Group Ia-3 (#206.37)
Go to the Systematic Absences for the Group Ia-3 (#206.37)

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