Bilbao Crystallographic Server arrow MGENPOS arrow Table of Magnetic Space Group Symbols Help

PIn-3 [#201.21] (Type: 4 -- Type IV (klassengleiche))

[OG: IPm'-3' #204.5.1534]

Operators of Group 201.21 (PIn-3)

1.x,y,z
mx,my,mz
( 
  1   0   0     0
  0   1   0     0
  0   0   1     0
 )
1 +1 {1|0,0,0}
2.-x+1/2,-y+1/2,z
-mx,-my,mz
( 
 -1   0   0   1/2
  0  -1   0   1/2
  0   0   1     0
 )
2 1/4,1/4,z +1 {2z|1/2,1/2,0}
3.-x+1/2,y,-z+1/2
-mx,my,-mz
( 
 -1   0   0   1/2
  0   1   0     0
  0   0  -1   1/2
 )
2 1/4,y,1/4 +1 {2y|1/2,0,1/2}
4.x,-y+1/2,-z+1/2
mx,-my,-mz
( 
  1   0   0     0
  0  -1   0   1/2
  0   0  -1   1/2
 )
2 x,1/4,1/4 +1 {2x|0,1/2,1/2}
5.z,x,y
mz,mx,my
( 
  0   0   1     0
  1   0   0     0
  0   1   0     0
 )
3+ x,x,x +1 {3xyz|0,0,0}
6.z,-x+1/2,-y+1/2
mz,-mx,-my
( 
  0   0   1     0
 -1   0   0   1/2
  0  -1   0   1/2
 )
3+ -x,x+1/2,-x +1 {3x-yz-1|0,1/2,1/2}
7.-z+1/2,-x+1/2,y
-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-xyz-1|1/2,1/2,0}
8.-z+1/2,x,-y+1/2
-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 {3xy-z-1|1/2,0,1/2}
9.y,z,x
my,mz,mx
( 
  0   1   0     0
  0   0   1     0
  1   0   0     0
 )
3- x,x,x +1 {3xyz-1|0,0,0}
10.-y+1/2,z,-x+1/2
-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-xyz|1/2,0,1/2}
11.y,-z+1/2,-x+1/2
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 {3xy-z|0,1/2,1/2}
12.-y+1/2,-z+1/2,x
-my,-mz,mx
( 
  0  -1   0   1/2
  0   0  -1   1/2
  1   0   0     0
 )
3- -x,x+1/2,-x +1 {3x-yz|1/2,1/2,0}
13.-x,-y,-z
mx,my,mz
( 
 -1   0   0     0
  0  -1   0     0
  0   0  -1     0
 )
-1 0,0,0 +1 {-1|0,0,0}
14.x+1/2,y+1/2,-z
-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 {mz|1/2,1/2,0}
15.x+1/2,-y,z+1/2
-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 {my|1/2,0,1/2}
16.-x,y+1/2,z+1/2
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 {mx|0,1/2,1/2}
17.-z,-x,-y
mz,mx,my
( 
  0   0  -1     0
 -1   0   0     0
  0  -1   0     0
 )
-3+ x,x,x 0,0,0 +1 {-3xyz|0,0,0}
18.-z,x+1/2,y+1/2
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 {-3x-yz-1|0,1/2,1/2}
19.z+1/2,x+1/2,-y
-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-xyz-1|1/2,1/2,0}
20.z+1/2,-x,y+1/2
-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 {-3xy-z-1|1/2,0,1/2}
21.-y,-z,-x
my,mz,mx
( 
  0  -1   0     0
  0   0  -1     0
 -1   0   0     0
 )
-3- x,x,x 0,0,0 +1 {-3xyz-1|0,0,0}
22.y+1/2,-z,x+1/2
-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-xyz|1/2,0,1/2}
23.-y,z+1/2,x+1/2
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 {-3xy-z|0,1/2,1/2}
24.y+1/2,z+1/2,-x
-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 {-3x-yz|1/2,1/2,0}
25.x+1/2,y+1/2,z+1/2
-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
-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 {2x|1/2,0,0}'
27.-x,y+1/2,-z
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 {2y|0,1/2,0}'
28.-x,-y,z+1/2
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 {2z|0,0,1/2}'
29.y+1/2,z+1/2,x+1/2
-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 {3xyz-1|1/2,1/2,1/2}'
30.y+1/2,-z,-x
-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 {3xy-z|1/2,0,0}'
31.-y,z+1/2,-x
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-xyz|0,1/2,0}'
32.-y,-z,x+1/2
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 {3x-yz|0,0,1/2}'
33.z+1/2,x+1/2,y+1/2
-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 {3xyz|1/2,1/2,1/2}'
34.z+1/2,-x,-y
-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 {3x-yz-1|1/2,0,0}'
35.-z,x+1/2,-y
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 {3xy-z-1|0,1/2,0}'
36.-z,-x,y+1/2
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-xyz-1|0,0,1/2}'
37.-x+1/2,-y+1/2,-z+1/2
-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
-mx,my,mz
( 
 -1   0   0   1/2
  0   1   0     0
  0   0   1     0
 ) '
m 1/4,y,z -1 {mx|1/2,0,0}'
39.x,-y+1/2,z
mx,-my,mz
( 
  1   0   0     0
  0  -1   0   1/2
  0   0   1     0
 ) '
m x,1/4,z -1 {my|0,1/2,0}'
40.x,y,-z+1/2
mx,my,-mz
( 
  1   0   0     0
  0   1   0     0
  0   0  -1   1/2
 ) '
m x,y,1/4 -1 {mz|0,0,1/2}'
41.-y+1/2,-z+1/2,-x+1/2
-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 {-3xyz-1|1/2,1/2,1/2}'
42.-y+1/2,z,x
-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 {-3xy-z|1/2,0,0}'
43.y,-z+1/2,x
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-xyz|0,1/2,0}'
44.y,z,-x+1/2
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 {-3x-yz|0,0,1/2}'
45.-z+1/2,-x+1/2,-y+1/2
-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 {-3xyz|1/2,1/2,1/2}'
46.-z+1/2,x,y
-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 {-3x-yz-1|1/2,0,0}'
47.z,-x+1/2,y
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 {-3xy-z-1|0,1/2,0}'
48.z,x,-y+1/2
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-xyz-1|0,0,1/2}'


Go to the Wyckoff Positions of 201.21 (PIn-3)
Go to the extinction rules of 201.21 (PIn-3)


Back to the list of magnetic space groups derived from Pn-3
Back to the list of Magnetic Space Groups

Bilbao Crystallographic Server
http://www.cryst.ehu.es 		For comments, please mail to
administrador.bcs@ehu.es