Bilbao Crystallographic Server MGENPOS General Positions of Magnetic Space Groups Help

## General Positions of the Group RI3c (#161.72) [BNS setting]

To display the general positions in the OG setting, please follow this link: RR3m' ( #160.5.1299) [Transformation matrix]

### Black-and-white lattice generators: (1|1,0,0), (1|0,1,0), (1|0,0,1), (1|2/3,1/3,1/3), (1|1/3,2/3,2/3), (1'|0,0,1/2) , (1'|2/3,1/3,5/6) , (1'|1/3,2/3,1/6)

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+1/2, +1
mx-my,-my,-mz
 ``` -1 1 0 0 0 1 0 0 0 0 1 1/2```
c x,2x,z +1 { m100 | 0 0 1/2 }
5 -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 { m110 | 0 0 1/2 }
6 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 2x,x,z +1 { m010 | 0 0 1/2 }
7 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 }
8 -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 }
9 -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 }
10 -x+y+2/3, y+1/3, z+5/6, +1
mx-my, -my, -mz
 ``` -1 1 0 2/3 0 1 0 1/3 0 0 1 5/6```
g (1/6,1/3,5/6) x+1/4,2x,z +1 { m100 | 2/3 1/3 5/6 }
11 -y+2/3, -x+1/3, z+5/6, +1
my, mx, -mz
 ``` 0 -1 0 2/3 -1 0 0 1/3 0 0 1 5/6```
g (1/6,-1/6,5/6) x+1/2,-x,z +1 { m110 | 2/3 1/3 5/6 }
12 x+2/3, x-y+1/3, z+5/6, +1
-mx, -mx+my, -mz
 ``` 1 0 0 2/3 1 -1 0 1/3 0 0 1 5/6```
g (2/3,1/3,5/6) 2x,x,z +1 { m010 | 2/3 1/3 5/6 }
13 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 }
14 -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 }
15 -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 }
16 -x+y+1/3, y+2/3, z+1/6, +1
mx-my, -my, -mz
 ``` -1 1 0 1/3 0 1 0 2/3 0 0 1 1/6```
g (1/3,2/3,1/6) x,2x,z +1 { m100 | 1/3 2/3 1/6 }
17 -y+1/3, -x+2/3, z+1/6, +1
my, mx, -mz
 ``` 0 -1 0 1/3 -1 0 0 2/3 0 0 1 1/6```
g (-1/6,1/6,1/6) x+1/2,-x,z +1 { m110 | 1/3 2/3 1/6 }
18 x+1/3, x-y+2/3, z+1/6, +1
-mx, -mx+my, -mz
 ``` 1 0 0 1/3 1 -1 0 2/3 0 0 1 1/6```
g (1/3,1/6,1/6) 2x-0.5,x,z +1 { m010 | 1/3 2/3 1/6 }
19 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 }
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+ (0,0,1/2) 0,0,z -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- (0,0,1/2) 0,0,z -1 { 3'-001 | 0 0 1/2 }
22 -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 { m'100 | 0 }
23 -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 }
24 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 { m'010 | 0 }
25 x+2/3, y+1/3, z+5/6, -1
-mx, -my, -mz
 ``` 1 0 0 2/3 0 1 0 1/3 0 0 1 5/6``` '
t (2/3,1/3,5/6) -1 { 1' | 2/3 1/3 5/6 }
26 -y+2/3, x-y+1/3, z+5/6, -1
my, -mx+my, -mz
 ``` 0 -1 0 2/3 1 -1 0 1/3 0 0 1 5/6``` '
3+ (0,0,5/6) 1/3,1/3,z -1 { 3'+001 | 2/3 1/3 5/6 }
27 -x+y+2/3, -x+1/3, z+5/6, -1
mx-my, mx, -mz
 ``` -1 1 0 2/3 -1 0 0 1/3 0 0 1 5/6``` '
3- (0,0,5/6) 1/3,0,z -1 { 3'-001 | 2/3 1/3 5/6 }
28 -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 { m'100 | 2/3 1/3 1/3 }
29 -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 { m'110 | 2/3 1/3 1/3 }
30 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 { m'010 | 2/3 1/3 1/3 }
31 x+1/3, y+2/3, z+1/6, -1
-mx, -my, -mz
 ``` 1 0 0 1/3 0 1 0 2/3 0 0 1 1/6``` '
t (1/3,2/3,1/6) -1 { 1' | 1/3 2/3 1/6 }
32 -y+1/3, x-y+2/3, z+1/6, -1
my, -mx+my, -mz
 ``` 0 -1 0 1/3 1 -1 0 2/3 0 0 1 1/6``` '
3+ (0,0,1/6) 0,1/3,z -1 { 3'+001 | 1/3 2/3 1/6 }
33 -x+y+1/3, -x+2/3, z+1/6, -1
mx-my, mx, -mz
 ``` -1 1 0 1/3 -1 0 0 2/3 0 0 1 1/6``` '
3- (0,0,1/6) 1/3,1/3,z -1 { 3'-001 | 1/3 2/3 1/6 }
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 { m'100 | 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 { m'110 | 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 { m'010 | 1/3 2/3 2/3 }

Go to the list of the Wyckoff Positions of the Group RI3c (#161.72)
Go to the Systematic Absences for the Group RI3c (#161.72)

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