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General Positions of the Group RI-3 (#148.20) [BNS setting]


To display the general positions in the OG setting, please follow this link: RR-3 ( #148.4.1250) [Transformation matrix]

Translation lattice generators: (1|1,0,0), (1|0,1,0), (1|0,0,1), (1|0,0,0), (1|2/3,1/3,1/3), (1|1/3,2/3,2/3)

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, -z, +1
mx,my,mz
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 +1 { -1 | 0 }
5 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 }
6 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 }
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+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 }
11 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 }
12 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 }
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+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 }
17 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 }
18 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 }
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, -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 }
23 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 }
24 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 }
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+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 }
29 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 }
30 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 }
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+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 }
35 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 }
36 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 }

Go to the list of the Wyckoff Positions of the Group RI-3 (#148.20)
Go to the Systematic Absences for the Group RI-3 (#148.20)

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