Bilbao Crystallographic Server MGENPOS General Positions of Magnetic Space Groups Help

## General Positions of the Group RI-3m (#166.102) [BNS setting]

To display the general positions in the OG setting, please follow this link: RR-3m ( #166.6.1332) [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
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 }
37 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 }
38 -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 }
39 -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 }
40 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,0,1/4 -1 { 2'100 | 0 0 1/2 }
41 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 { 2'110 | 0 0 1/2 }
42 -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 0,y,1/4 -1 { 2'010 | 0 0 1/2 }
43 -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 }
44 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 }
45 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 }
46 -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 { m'100 | 0 0 1/2 }
47 -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'110 | 0 0 1/2 }
48 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 { m'010 | 0 0 1/2 }
49 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 }
50 -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 }
51 -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 }
52 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``` '
2 (1/2,0,0) x,1/6,5/12 -1 { 2'100 | 2/3 1/3 5/6 }
53 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``` '
2 (1/2,1/2,0) x,x-0.16668,5/12 -1 { 2'110 | 2/3 1/3 5/6 }
54 -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``` '
2 1/3,y,5/12 -1 { 2'010 | 2/3 1/3 5/6 }
55 -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``` '
-1 1/3,1/6,5/12 -1 { -1' | 2/3 1/3 5/6 }
56 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+ 1/3,-1/3,z 1/3,-1/3,5/12 -1 { -3'+001 | 2/3 1/3 5/6 }
57 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- 1/3,2/3,z 1/3,2/3,5/12 -1 { -3'-001 | 2/3 1/3 5/6 }
58 -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 { m'100 | 2/3 1/3 5/6 }
59 -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 { m'110 | 2/3 1/3 5/6 }
60 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 { m'010 | 2/3 1/3 5/6 }
61 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 }
62 -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 }
63 -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 }
64 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``` '
2 x,1/3,1/12 -1 { 2'100 | 1/3 2/3 1/6 }
65 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``` '
2 (1/2,1/2,0) x,x+0.16668,1/12 -1 { 2'110 | 1/3 2/3 1/6 }
66 -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``` '
2 (0,1/2,0) 1/6,y,1/12 -1 { 2'010 | 1/3 2/3 1/6 }
67 -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``` '
-1 1/6,1/3,1/12 -1 { -1' | 1/3 2/3 1/6 }
68 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+ 2/3,1/3,z 2/3,1/3,1/12 -1 { -3'+001 | 1/3 2/3 1/6 }
69 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- -1/3,1/3,z -1/3,1/3,1/12 -1 { -3'-001 | 1/3 2/3 1/6 }
70 -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 { m'100 | 1/3 2/3 1/6 }
71 -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 { m'110 | 1/3 2/3 1/6 }
72 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 { m'010 | 1/3 2/3 1/6 }

Go to the list of the Wyckoff Positions of the Group RI-3m (#166.102)
Go to the Systematic Absences for the Group RI-3m (#166.102)

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