Bilbao Crystallographic Server MGENPOS General Positions of Magnetic Space Groups Help

## General Positions of the Group Pn-3m' (#224.113) For this space group, BNS and OG settings coincide.Its label in the OG setting is given as: Pn-3m' (#224.4.1614)

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+1/2, -z+1/2, +1
mx,-my,-mz
 ``` 1 0 0 0 0 -1 0 1/2 0 0 -1 1/2```
2 x,1/4,1/4 +1 { 2100 | 0 1/2 1/2 }
3 -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 1/4,y,1/4 +1 { 2010 | 1/2 0 1/2 }
4 -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 1/4,1/4,z +1 { 2001 | 1/2 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+1/2, +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 { 3-1-1-1 | 1/2 0 1/2 }
8 -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+1-1-1 | 1/2 1/2 0 }
9 -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 +1 { 3--11-1 | 1/2 1/2 0 }
10 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+-11-1 | 0 1/2 1/2 }
11 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+1/2,x +1 { 3--1-11 | 0 1/2 1/2 }
12 -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 { 3+-1-11 | 1/2 0 1/2 }
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+1/2, z+1/2, +1
mx,-my,-mz
 ``` -1 0 0 0 0 1 0 1/2 0 0 1 1/2```
n (0,1/2,1/2) 0,y,z +1 { m100 | 0 1/2 1/2 }
15 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```
n (1/2,0,1/2) x,0,z +1 { m010 | 1/2 0 1/2 }
16 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```
n (1/2,1/2,0) x,y,0 +1 { m001 | 1/2 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+1/2, +1
-my,mz,-mx
 ``` 0 1 0 1/2 0 0 -1 0 1 0 0 1/2```
-3- x+1/2,-x,-x 0,-1/2,1/2 +1 { -3-1-1-1 | 1/2 0 1/2 }
20 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-0.5,-x+1,-x 0,1/2,-1/2 +1 { -3+1-1-1 | 1/2 1/2 0 }
21 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+1,x-1/2,-x 1/2,0,-1/2 +1 { -3--11-1 | 1/2 1/2 0 }
22 -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+-11-1 | 0 1/2 1/2 }
23 -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+1/2,x -1/2,1/2,0 +1 { -3--1-11 | 0 1/2 1/2 }
24 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 1/2,-1/2,0 +1 { -3+-1-11 | 1/2 0 1/2 }
25 x+1/2, -z, y+1/2, -1
-mx,mz,-my
 ``` 1 0 0 1/2 0 0 -1 0 0 1 0 1/2``` '
4+ (1/2,0,0) x,-1/4,1/4 -1 { 4'+100 | 1/2 0 1/2 }
26 x+1/2, z+1/2, -y, -1
-mx,-mz,my
 ``` 1 0 0 1/2 0 0 1 1/2 0 -1 0 0``` '
4- (1/2,0,0) x,1/4,-1/4 -1 { 4'-100 | 1/2 1/2 0 }
27 z+1/2, y+1/2, -x, -1
-mz,-my,mx
 ``` 0 0 1 1/2 0 1 0 1/2 -1 0 0 0``` '
4+ (0,1/2,0) 1/4,y,-1/4 -1 { 4'+010 | 1/2 1/2 0 }
28 -z, y+1/2, x+1/2, -1
mz,-my,-mx
 ``` 0 0 -1 0 0 1 0 1/2 1 0 0 1/2``` '
4- (0,1/2,0) -1/4,y,1/4 -1 { 4'-010 | 0 1/2 1/2 }
29 -y, x+1/2, z+1/2, -1
my,-mx,-mz
 ``` 0 -1 0 0 1 0 0 1/2 0 0 1 1/2``` '
4+ (0,0,1/2) -1/4,1/4,z -1 { 4'+001 | 0 1/2 1/2 }
30 y+1/2, -x, z+1/2, -1
-my,mx,-mz
 ``` 0 1 0 1/2 -1 0 0 0 0 0 1 1/2``` '
4- (0,0,1/2) 1/4,-1/4,z -1 { 4'-001 | 1/2 0 1/2 }
31 y+1/2, x+1/2, -z, -1
-my,-mx,mz
 ``` 0 1 0 1/2 1 0 0 1/2 0 0 -1 0``` '
2 (1/2,1/2,0) x,x,0 -1 { 2'110 | 1/2 1/2 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+1/2, y+1/2, -1
mx,-mz,-my
 ``` -1 0 0 0 0 0 1 1/2 0 1 0 1/2``` '
2 (0,1/2,1/2) 0,y,y -1 { 2'011 | 0 1/2 1/2 }
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+1/2, -y, x+1/2, -1
-mz,my,-mx
 ``` 0 0 1 1/2 0 -1 0 0 1 0 0 1/2``` '
2 (1/2,0,1/2) x,0,x -1 { 2'101 | 1/2 0 1/2 }
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+1/2, z, -y+1/2, -1
-mx,mz,-my
 ``` -1 0 0 1/2 0 0 1 0 0 -1 0 1/2``` '
-4+ x,1/4,1/4 1/4,1/4,1/4 -1 { -4'+100 | 1/2 0 1/2 }
38 -x+1/2, -z+1/2, y, -1
-mx,-mz,my
 ``` -1 0 0 1/2 0 0 -1 1/2 0 1 0 0``` '
-4- x,1/4,1/4 1/4,1/4,1/4 -1 { -4'-100 | 1/2 1/2 0 }
39 -z+1/2, -y+1/2, x, -1
-mz,-my,mx
 ``` 0 0 -1 1/2 0 -1 0 1/2 1 0 0 0``` '
-4+ 1/4,y,1/4 1/4,1/4,1/4 -1 { -4'+010 | 1/2 1/2 0 }
40 z, -y+1/2, -x+1/2, -1
mz,-my,-mx
 ``` 0 0 1 0 0 -1 0 1/2 -1 0 0 1/2``` '
-4- 1/4,y,1/4 1/4,1/4,1/4 -1 { -4'-010 | 0 1/2 1/2 }
41 y, -x+1/2, -z+1/2, -1
my,-mx,-mz
 ``` 0 1 0 0 -1 0 0 1/2 0 0 -1 1/2``` '
-4+ 1/4,1/4,z 1/4,1/4,1/4 -1 { -4'+001 | 0 1/2 1/2 }
42 -y+1/2, x, -z+1/2, -1
-my,mx,-mz
 ``` 0 -1 0 1/2 1 0 0 0 0 0 -1 1/2``` '
-4- 1/4,1/4,z 1/4,1/4,1/4 -1 { -4'-001 | 1/2 0 1/2 }
43 -y+1/2, -x+1/2, z, -1
-my,-mx,mz
 ``` 0 -1 0 1/2 -1 0 0 1/2 0 0 1 0``` '
m x+1/2,-x,z -1 { m'110 | 1/2 1/2 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+1/2, -y+1/2, -1
mx,-mz,-my
 ``` 1 0 0 0 0 0 -1 1/2 0 -1 0 1/2``` '
m x,y+1/2,-y -1 { m'011 | 0 1/2 1/2 }
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+1/2, y, -x+1/2, -1
-mz,my,-mx
 ``` 0 0 -1 1/2 0 1 0 0 -1 0 0 1/2``` '
m -x+1/2,y,x -1 { m'101 | 1/2 0 1/2 }
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 }

Go to the list of the Wyckoff Positions of the Group Pn-3m' (#224.113)
Go to the Systematic Absences for the Group Pn-3m' (#224.113)

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