Bilbao Crystallographic Server MGENPOS General Positions of Magnetic Space Groups Help

## General Positions of the Group R-3m (#166.97) For this space group, BNS and OG settings coincide.Its label in the OG setting is given as: R-3m (#166.1.1327)

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-y, -y, -z, +1
mx-my,-my,-mz
 ``` 1 -1 0 0 0 -1 0 0 0 0 -1 0```
2 x,0,0 +1 { 2100 | 0 }
5 y, x, -z, +1
my,mx,-mz
 ``` 0 1 0 0 1 0 0 0 0 0 -1 0```
2 x,x,0 +1 { 2110 | 0 }
6 -x, -x+y, -z, +1
-mx,-mx+my,-mz
 ``` -1 0 0 0 -1 1 0 0 0 0 -1 0```
2 0,y,0 +1 { 2010 | 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+y, y, z, +1
mx-my,-my,-mz
 ``` -1 1 0 0 0 1 0 0 0 0 1 0```
m x,2x,z +1 { m100 | 0 }
11 -y, -x, z, +1
my,mx,-mz
 ``` 0 -1 0 0 -1 0 0 0 0 0 1 0```
m x,-x,z +1 { m110 | 0 }
12 x, x-y, z, +1
-mx,-mx+my,-mz
 ``` 1 0 0 0 1 -1 0 0 0 0 1 0```
m 2x,x,z +1 { m010 | 0 }
13 x+2/3, y+1/3, z+1/3, +1
mx,my,mz
 ``` 1 0 0 2/3 0 1 0 1/3 0 0 1 1/3```
t (2/3,1/3,1/3) +1 { 1 | 2/3 1/3 1/3 }
14 -y+2/3, x-y+1/3, z+1/3, +1
-my,mx-my,mz
 ``` 0 -1 0 2/3 1 -1 0 1/3 0 0 1 1/3```
3+ (0,0,1/3) 1/3,1/3,z +1 { 3+001 | 2/3 1/3 1/3 }
15 -x+y+2/3, -x+1/3, z+1/3, +1
-mx+my,-mx,mz
 ``` -1 1 0 2/3 -1 0 0 1/3 0 0 1 1/3```
3- (0,0,1/3) 1/3,0,z +1 { 3-001 | 2/3 1/3 1/3 }
16 x-y+2/3, -y+1/3, -z+1/3, +1
mx-my,-my,-mz
 ``` 1 -1 0 2/3 0 -1 0 1/3 0 0 -1 1/3```
2 (1/2,0,0) x,1/6,1/6 +1 { 2100 | 2/3 1/3 1/3 }
17 y+2/3, x+1/3, -z+1/3, +1
my,mx,-mz
 ``` 0 1 0 2/3 1 0 0 1/3 0 0 -1 1/3```
2 (1/2,1/2,0) x,x-0.16668,1/6 +1 { 2110 | 2/3 1/3 1/3 }
18 -x+2/3, -x+y+1/3, -z+1/3, +1
-mx,-mx+my,-mz
 ``` -1 0 0 2/3 -1 1 0 1/3 0 0 -1 1/3```
2 1/3,y,1/6 +1 { 2010 | 2/3 1/3 1/3 }
19 -x+2/3, -y+1/3, -z+1/3, +1
mx, my, mz
 ``` -1 0 0 2/3 0 -1 0 1/3 0 0 -1 1/3```
-1 1/3,1/6,1/6 +1 { -1 | 2/3 1/3 1/3 }
20 y+2/3, -x+y+1/3, -z+1/3, +1
-my, mx-my, mz
 ``` 0 1 0 2/3 -1 1 0 1/3 0 0 -1 1/3```
-3+ 1/3,-1/3,z 1/3,-1/3,1/6 +1 { -3+001 | 2/3 1/3 1/3 }
21 x-y+2/3, x+1/3, -z+1/3, +1
-mx+my, -mx, mz
 ``` 1 -1 0 2/3 1 0 0 1/3 0 0 -1 1/3```
-3- 1/3,2/3,z 1/3,2/3,1/6 +1 { -3-001 | 2/3 1/3 1/3 }
22 -x+y+2/3, y+1/3, z+1/3, +1
mx-my, -my, -mz
 ``` -1 1 0 2/3 0 1 0 1/3 0 0 1 1/3```
g (1/6,1/3,1/3) x+1/4,2x,z +1 { m100 | 2/3 1/3 1/3 }
23 -y+2/3, -x+1/3, z+1/3, +1
my, mx, -mz
 ``` 0 -1 0 2/3 -1 0 0 1/3 0 0 1 1/3```
g (1/6,-1/6,1/3) x+1/2,-x,z +1 { m110 | 2/3 1/3 1/3 }
24 x+2/3, x-y+1/3, z+1/3, +1
-mx, -mx+my, -mz
 ``` 1 0 0 2/3 1 -1 0 1/3 0 0 1 1/3```
g (2/3,1/3,1/3) 2x,x,z +1 { m010 | 2/3 1/3 1/3 }
25 x+1/3, y+2/3, z+2/3, +1
mx,my,mz
 ``` 1 0 0 1/3 0 1 0 2/3 0 0 1 2/3```
t (1/3,2/3,2/3) +1 { 1 | 1/3 2/3 2/3 }
26 -y+1/3, x-y+2/3, z+2/3, +1
-my,mx-my,mz
 ``` 0 -1 0 1/3 1 -1 0 2/3 0 0 1 2/3```
3+ (0,0,2/3) 0,1/3,z +1 { 3+001 | 1/3 2/3 2/3 }
27 -x+y+1/3, -x+2/3, z+2/3, +1
-mx+my,-mx,mz
 ``` -1 1 0 1/3 -1 0 0 2/3 0 0 1 2/3```
3- (0,0,2/3) 1/3,1/3,z +1 { 3-001 | 1/3 2/3 2/3 }
28 x-y+1/3, -y+2/3, -z+2/3, +1
mx-my,-my,-mz
 ``` 1 -1 0 1/3 0 -1 0 2/3 0 0 -1 2/3```
2 x,1/3,1/3 +1 { 2100 | 1/3 2/3 2/3 }
29 y+1/3, x+2/3, -z+2/3, +1
my,mx,-mz
 ``` 0 1 0 1/3 1 0 0 2/3 0 0 -1 2/3```
2 (1/2,1/2,0) x,x+0.16668,1/3 +1 { 2110 | 1/3 2/3 2/3 }
30 -x+1/3, -x+y+2/3, -z+2/3, +1
-mx,-mx+my,-mz
 ``` -1 0 0 1/3 -1 1 0 2/3 0 0 -1 2/3```
2 (0,1/2,0) 1/6,y,1/3 +1 { 2010 | 1/3 2/3 2/3 }
31 -x+1/3, -y+2/3, -z+2/3, +1
mx, my, mz
 ``` -1 0 0 1/3 0 -1 0 2/3 0 0 -1 2/3```
-1 1/6,1/3,1/3 +1 { -1 | 1/3 2/3 2/3 }
32 y+1/3, -x+y+2/3, -z+2/3, +1
-my, mx-my, mz
 ``` 0 1 0 1/3 -1 1 0 2/3 0 0 -1 2/3```
-3+ 2/3,1/3,z 2/3,1/3,1/3 +1 { -3+001 | 1/3 2/3 2/3 }
33 x-y+1/3, x+2/3, -z+2/3, +1
-mx+my, -mx, mz
 ``` 1 -1 0 1/3 1 0 0 2/3 0 0 -1 2/3```
-3- -1/3,1/3,z -1/3,1/3,1/3 +1 { -3-001 | 1/3 2/3 2/3 }
34 -x+y+1/3, y+2/3, z+2/3, +1
mx-my, -my, -mz
 ``` -1 1 0 1/3 0 1 0 2/3 0 0 1 2/3```
g (1/3,2/3,2/3) x,2x,z +1 { m100 | 1/3 2/3 2/3 }
35 -y+1/3, -x+2/3, z+2/3, +1
my, mx, -mz
 ``` 0 -1 0 1/3 -1 0 0 2/3 0 0 1 2/3```
g (-1/6,1/6,2/3) x+1/2,-x,z +1 { m110 | 1/3 2/3 2/3 }
36 x+1/3, x-y+2/3, z+2/3, +1
-mx, -mx+my, -mz
 ``` 1 0 0 1/3 1 -1 0 2/3 0 0 1 2/3```
g (1/3,1/6,2/3) 2x-0.5,x,z +1 { m010 | 1/3 2/3 2/3 }

Go to the list of the Wyckoff Positions of the Group R-3m (#166.97)
Go to the Systematic Absences for the Group R-3m (#166.97)

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