Bilbao Crystallographic Server MGENPOS General Positions of Magnetic Space Groups Help

## General Positions of the Group PC42/ncm (#138.529) [BNS setting]

To display the general positions in the OG setting, please follow this link: PP42/m'mc ( #131.11.1107) [Transformation matrix]

### Black-and-white lattice generators: (1|1,0,0), (1|0,1,0), (1|0,0,1), (1'|1/2,1/2,0)

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 -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 }
3 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 }
4 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 (1/2,0,0) x,0,1/4 +1 { 2100 | 1/2 0 1/2 }
5 -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 }
6 -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 }
7 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 { 2110 | 1/2 1/2 0 }
8 -y, -x, -z, +1
-my,-mx,-mz
 ``` 0 -1 0 0 -1 0 0 0 0 0 -1 0```
2 x,-x,0 +1 { 21-10 | 0 }
9 -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 }
10 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 }
11 -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 }
12 -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```
c 1/4,y,z +1 { m100 | 1/2 0 1/2 }
13 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 }
14 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 }
15 -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 { m110 | 1/2 1/2 0 }
16 y, x, z, +1
-my,-mx,-mz
 ``` 0 1 0 0 1 0 0 0 0 0 1 0```
m x,x,z +1 { m1-10 | 0 }
17 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``` '
t (1/2,1/2,0) -1 { 1' | 1/2 1/2 0 }
18 -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 }
19 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 }
20 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 { 2'100 | 0 1/2 1/2 }
21 -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 { 2'010 | 1/2 0 1/2 }
22 -x, -y, z, -1
mx,my,-mz
 ``` -1 0 0 0 0 -1 0 0 0 0 1 0``` '
2 0,0,z -1 { 2'001 | 0 }
23 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 }
24 -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 x,-x+1/2,0 -1 { 2'1-10 | 1/2 1/2 0 }
25 -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``` '
-1 1/4,1/4,0 -1 { -1' | 1/2 1/2 0 }
26 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 }
27 -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 }
28 -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 { m'100 | 0 1/2 1/2 }
29 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 { m'010 | 1/2 0 1/2 }
30 x, y, -z, -1
mx,my,-mz
 ``` 1 0 0 0 0 1 0 0 0 0 -1 0``` '
m x,y,0 -1 { m'001 | 0 }
31 -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 }
32 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``` '
g (1/2,1/2,0) x,x,z -1 { m'1-10 | 1/2 1/2 0 }

Go to the list of the Wyckoff Positions of the Group PC42/ncm (#138.529)
Go to the Systematic Absences for the Group PC42/ncm (#138.529)

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