Bilbao Crystallographic Server MGENPOS General Positions of Magnetic Space Groups Help

## General Positions of the Group Pc-31m (#162.78) [BNS setting]

To display the general positions in the OG setting, please follow this link: P2c-31m ( #162.6.1308) [Transformation matrix]

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

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, x-y, z, +1
-my,mx-my,mz
 ``` 0 -1 0 0 1 -1 0 0 0 0 1 0```
3+ 0,0,z +1 { 3+001 | 0 }
3 -x+y, -x, z, +1
-mx+my,-mx,mz
 ``` -1 1 0 0 -1 0 0 0 0 0 1 0```
3- 0,0,z +1 { 3-001 | 0 }
4 x, x-y, -z, +1
mx,mx-my,-mz
 ``` 1 0 0 0 1 -1 0 0 0 0 -1 0```
2 2x,x,0 +1 { 2210 | 0 }
5 -x+y, y, -z, +1
-mx+my,my,-mz
 ``` -1 1 0 0 0 1 0 0 0 0 -1 0```
2 x,2x,0 +1 { 2120 | 0 }
6 -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 }
7 -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 }
8 y, -x+y, -z, +1
-my,mx-my,mz
 ``` 0 1 0 0 -1 1 0 0 0 0 -1 0```
-3+ 0,0,z 0,0,0 +1 { -3+001 | 0 }
9 x-y, x, -z, +1
-mx+my,-mx,mz
 ``` 1 -1 0 0 1 0 0 0 0 0 -1 0```
-3- 0,0,z 0,0,0 +1 { -3-001 | 0 }
10 -x, -x+y, z, +1
mx,mx-my,-mz
 ``` -1 0 0 0 -1 1 0 0 0 0 1 0```
m 0,y,z +1 { m210 | 0 }
11 x-y, -y, z, +1
-mx+my,my,-mz
 ``` 1 -1 0 0 0 -1 0 0 0 0 1 0```
m x,0,z +1 { m120 | 0 }
12 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 }
13 x, y, z+1/2, -1
-mx,-my,-mz
 ``` 1 0 0 0 0 1 0 0 0 0 1 1/2``` '
t (0,0,1/2) -1 { 1' | 0 0 1/2 }
14 -y, x-y, z+1/2, -1
my,-mx+my,-mz
 ``` 0 -1 0 0 1 -1 0 0 0 0 1 1/2``` '
3+ (0,0,1/2) 0,0,z -1 { 3'+001 | 0 0 1/2 }
15 -x+y, -x, z+1/2, -1
mx-my,mx,-mz
 ``` -1 1 0 0 -1 0 0 0 0 0 1 1/2``` '
3- (0,0,1/2) 0,0,z -1 { 3'-001 | 0 0 1/2 }
16 x, x-y, -z+1/2, -1
-mx,-mx+my,mz
 ``` 1 0 0 0 1 -1 0 0 0 0 -1 1/2``` '
2 2x,x,1/4 -1 { 2'210 | 0 0 1/2 }
17 -x+y, y, -z+1/2, -1
mx-my,-my,mz
 ``` -1 1 0 0 0 1 0 0 0 0 -1 1/2``` '
2 x,2x,1/4 -1 { 2'120 | 0 0 1/2 }
18 -y, -x, -z+1/2, -1
my,mx,mz
 ``` 0 -1 0 0 -1 0 0 0 0 0 -1 1/2``` '
2 x,-x,1/4 -1 { 2'1-10 | 0 0 1/2 }
19 -x, -y, -z+1/2, -1
-mx,-my,-mz
 ``` -1 0 0 0 0 -1 0 0 0 0 -1 1/2``` '
-1 0,0,1/4 -1 { -1' | 0 0 1/2 }
20 y, -x+y, -z+1/2, -1
my,-mx+my,-mz
 ``` 0 1 0 0 -1 1 0 0 0 0 -1 1/2``` '
-3+ 0,0,z 0,0,1/4 -1 { -3'+001 | 0 0 1/2 }
21 x-y, x, -z+1/2, -1
mx-my,mx,-mz
 ``` 1 -1 0 0 1 0 0 0 0 0 -1 1/2``` '
-3- 0,0,z 0,0,1/4 -1 { -3'-001 | 0 0 1/2 }
22 -x, -x+y, z+1/2, -1
-mx,-mx+my,mz
 ``` -1 0 0 0 -1 1 0 0 0 0 1 1/2``` '
c 0,y,z -1 { m'210 | 0 0 1/2 }
23 x-y, -y, z+1/2, -1
mx-my,-my,mz
 ``` 1 -1 0 0 0 -1 0 0 0 0 1 1/2``` '
c x,0,z -1 { m'120 | 0 0 1/2 }
24 y, x, z+1/2, -1
my,mx,mz
 ``` 0 1 0 0 1 0 0 0 0 0 1 1/2``` '
c x,x,z -1 { m'1-10 | 0 0 1/2 }

Go to the list of the Wyckoff Positions of the Group Pc-31m (#162.78)
Go to the Systematic Absences for the Group Pc-31m (#162.78)

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