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General Positions of the Group PIn-3 (#201.21) [BNS setting]

201.21 Pn-3.1'I[Im-3] (UNI symbol)

To display the general positions in the OG setting, please follow this link: IPm'-3' ( #204.5.1534) [Transformation matrix]

Translation lattice generators: (1|1,0,0), (1|0,1,0), (1|0,0,1), (1|0,0,0)

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

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 x, -y+1/2, -z+1/2, +1
mx,-my,-mz
(
   1   0   0    0
   0  -1   0   1/2
   0   0  -1   1/2
)
 2 x,1/4,1/4 +1 { 2100 | 0 1/2 1/2 }
3 -x+1/2, y, -z+1/2, +1
-mx,my,-mz
(
  -1   0   0   1/2
   0   1   0    0
   0   0  -1   1/2
)
 2 1/4,y,1/4 +1 { 2010 | 1/2 0 1/2 }
4 -x+1/2, -y+1/2, z, +1
-mx,-my,mz
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0   1    0
)
 2 1/4,1/4,z +1 { 2001 | 1/2 1/2 0 }
5 z, x, y, +1
mz,mx,my
(
   0   0   1    0
   1   0   0    0
   0   1   0    0
)
 3+ x,x,x +1 { 3+111 | 0 }
6 y, z, x, +1
my,mz,mx
(
   0   1   0    0
   0   0   1    0
   1   0   0    0
)
 3- x,x,x +1 { 3-111 | 0 }
7 -y+1/2, z, -x+1/2, +1
-my,mz,-mx
(
   0  -1   0   1/2
   0   0   1    0
  -1   0   0   1/2
)
 3- x+1/2,-x,-x +1 { 3-1-1-1 | 1/2 0 1/2 }
8 -z+1/2, -x+1/2, y, +1
-mz,-mx,my
(
   0   0  -1   1/2
  -1   0   0   1/2
   0   1   0    0
)
 3+ x+1/2,-x,-x +1 { 3+1-1-1 | 1/2 1/2 0 }
9 -y+1/2, -z+1/2, x, +1
-my,-mz,mx
(
   0  -1   0   1/2
   0   0  -1   1/2
   1   0   0    0
)
 3- -x,x+1/2,-x +1 { 3--11-1 | 1/2 1/2 0 }
10 z, -x+1/2, -y+1/2, +1
mz,-mx,-my
(
   0   0   1    0
  -1   0   0   1/2
   0  -1   0   1/2
)
 3+ -x,x+1/2,-x +1 { 3+-11-1 | 0 1/2 1/2 }
11 y, -z+1/2, -x+1/2, +1
my,-mz,-mx
(
   0   1   0    0
   0   0  -1   1/2
  -1   0   0   1/2
)
 3- -x+1/2,-x+1/2,x +1 { 3--1-11 | 0 1/2 1/2 }
12 -z+1/2, x, -y+1/2, +1
-mz,mx,-my
(
   0   0  -1   1/2
   1   0   0    0
   0  -1   0   1/2
)
 3+ -x+1/2,-x+1/2,x +1 { 3+-1-11 | 1/2 0 1/2 }
13 -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 }
14 -x, y+1/2, z+1/2, +1
mx,-my,-mz
(
  -1   0   0    0
   0   1   0   1/2
   0   0   1   1/2
)
 n (0,1/2,1/2) 0,y,z +1 { m100 | 0 1/2 1/2 }
15 x+1/2, -y, z+1/2, +1
-mx,my,-mz
(
   1   0   0   1/2
   0  -1   0    0
   0   0   1   1/2
)
 n (1/2,0,1/2) x,0,z +1 { m010 | 1/2 0 1/2 }
16 x+1/2, y+1/2, -z, +1
-mx,-my,mz
(
   1   0   0   1/2
   0   1   0   1/2
   0   0  -1    0
)
 n (1/2,1/2,0) x,y,0 +1 { m001 | 1/2 1/2 0 }
17 -z, -x, -y, +1
mz,mx,my
(
   0   0  -1    0
  -1   0   0    0
   0  -1   0    0
)
 -3+ x,x,x 0,0,0 +1 { -3+111 | 0 }
18 -y, -z, -x, +1
my,mz,mx
(
   0  -1   0    0
   0   0  -1    0
  -1   0   0    0
)
 -3- x,x,x 0,0,0 +1 { -3-111 | 0 }
19 y+1/2, -z, x+1/2, +1
-my,mz,-mx
(
   0   1   0   1/2
   0   0  -1    0
   1   0   0   1/2
)
 -3- x+1/2,-x,-x 0,-1/2,1/2 +1 { -3-1-1-1 | 1/2 0 1/2 }
20 z+1/2, x+1/2, -y, +1
-mz,-mx,my
(
   0   0   1   1/2
   1   0   0   1/2
   0  -1   0    0
)
 -3+ x-0.5,-x+1,-x 0,1/2,-1/2 +1 { -3+1-1-1 | 1/2 1/2 0 }
21 y+1/2, z+1/2, -x, +1
-my,-mz,mx
(
   0   1   0   1/2
   0   0   1   1/2
  -1   0   0    0
)
 -3- -x+1,x-1/2,-x 1/2,0,-1/2 +1 { -3--11-1 | 1/2 1/2 0 }
22 -z, x+1/2, y+1/2, +1
mz,-mx,-my
(
   0   0  -1    0
   1   0   0   1/2
   0   1   0   1/2
)
 -3+ -x-1,x+1/2,-x -1/2,0,1/2 +1 { -3+-11-1 | 0 1/2 1/2 }
23 -y, z+1/2, x+1/2, +1
my,-mz,-mx
(
   0  -1   0    0
   0   0   1   1/2
   1   0   0   1/2
)
 -3- -x-1/2,-x+1/2,x -1/2,1/2,0 +1 { -3--1-11 | 0 1/2 1/2 }
24 z+1/2, -x, y+1/2, +1
-mz,mx,-my
(
   0   0   1   1/2
  -1   0   0    0
   0   1   0   1/2
)
 -3+ -x+1/2,-x,x 1/2,-1/2,0 +1 { -3+-1-11 | 1/2 0 1/2 }
25 x+1/2, y+1/2, z+1/2, -1
-mx,-my,-mz
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1   1/2
)'
 t (1/2,1/2,1/2) -1 { 1' | 1/2 1/2 1/2 }
26 x+1/2, -y, -z, -1
-mx,my,mz
(
   1   0   0   1/2
   0  -1   0    0
   0   0  -1    0
)'
 2 (1/2,0,0) x,0,0 -1 { 2'100 | 1/2 0 0 }
27 -x, y+1/2, -z, -1
mx,-my,mz
(
  -1   0   0    0
   0   1   0   1/2
   0   0  -1    0
)'
 2 (0,1/2,0) 0,y,0 -1 { 2'010 | 0 1/2 0 }
28 -x, -y, z+1/2, -1
mx,my,-mz
(
  -1   0   0    0
   0  -1   0    0
   0   0   1   1/2
)'
 2 (0,0,1/2) 0,0,z -1 { 2'001 | 0 0 1/2 }
29 z+1/2, x+1/2, y+1/2, -1
-mz,-mx,-my
(
   0   0   1   1/2
   1   0   0   1/2
   0   1   0   1/2
)'
 3+ (1/2,1/2,1/2) x,x,x -1 { 3'+111 | 1/2 1/2 1/2 }
30 y+1/2, z+1/2, x+1/2, -1
-my,-mz,-mx
(
   0   1   0   1/2
   0   0   1   1/2
   1   0   0   1/2
)'
 3- (1/2,1/2,1/2) x,x,x -1 { 3'-111 | 1/2 1/2 1/2 }
31 -y, z+1/2, -x, -1
my,-mz,mx
(
   0  -1   0    0
   0   0   1   1/2
  -1   0   0    0
)'
 3- (-1/6,1/6,1/6) x-0.16667,-x+1/3,-x -1 { 3'-1-1-1 | 0 1/2 0 }
32 -z, -x, y+1/2, -1
mz,mx,-my
(
   0   0  -1    0
  -1   0   0    0
   0   1   0   1/2
)'
 3+ (-1/6,1/6,1/6) x+1/6,-x,-x -1 { 3'+1-1-1 | 0 0 1/2 }
33 -y, -z, x+1/2, -1
my,mz,-mx
(
   0  -1   0    0
   0   0  -1    0
   1   0   0   1/2
)'
 3- (1/6,-1/6,1/6) -x-1/3,x+1/6,-x -1 { 3'--11-1 | 0 0 1/2 }
34 z+1/2, -x, -y, -1
-mz,mx,my
(
   0   0   1   1/2
  -1   0   0    0
   0  -1   0    0
)'
 3+ (1/6,-1/6,1/6) -x+1/3,x-1/6,-x -1 { 3'+-11-1 | 1/2 0 0 }
35 y+1/2, -z, -x, -1
-my,mz,mx
(
   0   1   0   1/2
   0   0  -1    0
  -1   0   0    0
)'
 3- (1/6,1/6,-1/6) -x+1/6,-x,x -1 { 3'--1-11 | 1/2 0 0 }
36 -z, x+1/2, -y, -1
mz,-mx,my
(
   0   0  -1    0
   1   0   0   1/2
   0  -1   0    0
)'
 3+ (1/6,1/6,-1/6) -x-1/6,-x+1/6,x -1 { 3'+-1-11 | 0 1/2 0 }
37 -x+1/2, -y+1/2, -z+1/2, -1
-mx,-my,-mz
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1   1/2
)'
 -1 1/4,1/4,1/4 -1 { -1' | 1/2 1/2 1/2 }
38 -x+1/2, y, z, -1
-mx,my,mz
(
  -1   0   0   1/2
   0   1   0    0
   0   0   1    0
)'
 m 1/4,y,z -1 { m'100 | 1/2 0 0 }
39 x, -y+1/2, z, -1
mx,-my,mz
(
   1   0   0    0
   0  -1   0   1/2
   0   0   1    0
)'
 m x,1/4,z -1 { m'010 | 0 1/2 0 }
40 x, y, -z+1/2, -1
mx,my,-mz
(
   1   0   0    0
   0   1   0    0
   0   0  -1   1/2
)'
 m x,y,1/4 -1 { m'001 | 0 0 1/2 }
41 -z+1/2, -x+1/2, -y+1/2, -1
-mz,-mx,-my
(
   0   0  -1   1/2
  -1   0   0   1/2
   0  -1   0   1/2
)'
 -3+ x,x,x 1/4,1/4,1/4 -1 { -3'+111 | 1/2 1/2 1/2 }
42 -y+1/2, -z+1/2, -x+1/2, -1
-my,-mz,-mx
(
   0  -1   0   1/2
   0   0  -1   1/2
  -1   0   0   1/2
)'
 -3- x,x,x 1/4,1/4,1/4 -1 { -3'-111 | 1/2 1/2 1/2 }
43 y, -z+1/2, x, -1
my,-mz,mx
(
   0   1   0    0
   0   0  -1   1/2
   1   0   0    0
)'
 -3- x+1/2,-x,-x 1/4,1/4,1/4 -1 { -3'-1-1-1 | 0 1/2 0 }
44 z, x, -y+1/2, -1
mz,mx,-my
(
   0   0   1    0
   1   0   0    0
   0  -1   0   1/2
)'
 -3+ x+1/2,-x,-x 1/4,1/4,1/4 -1 { -3'+1-1-1 | 0 0 1/2 }
45 y, z, -x+1/2, -1
my,mz,-mx
(
   0   1   0    0
   0   0   1    0
  -1   0   0   1/2
)'
 -3- -x,x+1/2,-x 1/4,1/4,1/4 -1 { -3'--11-1 | 0 0 1/2 }
46 -z+1/2, x, y, -1
-mz,mx,my
(
   0   0  -1   1/2
   1   0   0    0
   0   1   0    0
)'
 -3+ -x,x+1/2,-x 1/4,1/4,1/4 -1 { -3'+-11-1 | 1/2 0 0 }
47 -y+1/2, z, x, -1
-my,mz,mx
(
   0  -1   0   1/2
   0   0   1    0
   1   0   0    0
)'
 -3- -x+1/2,-x+1/2,x 1/4,1/4,1/4 -1 { -3'--1-11 | 1/2 0 0 }
48 z, -x+1/2, y, -1
mz,-mx,my
(
   0   0   1    0
  -1   0   0   1/2
   0   1   0    0
)'
 -3+ -x+1/2,-x+1/2,x 1/4,1/4,1/4 -1 { -3'+-1-11 | 0 1/2 0 }

Go to the list of the Wyckoff Positions of the Group PIn-3 (#201.21)
Go to the Systematic Absences for the Group PIn-3 (#201.21)

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