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Pn-3m' [#224.113] (Type: 3 -- Type III (translationgleiche))

[OG: Pn-3m' #224.4.1614]

Operators of Group 224.113 (Pn-3m')

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.y+1/2,x+1/2,-z
-my,-mx,mz
( 
  0   1   0   1/2
  1   0   0   1/2
  0   0  -1     0
 ) '
2 (1/2,1/2,0) x,x,0 -1 {2xy|1/2,1/2,0}'
26.-y,-x,-z
my,mx,mz
( 
  0  -1   0     0
 -1   0   0     0
  0   0  -1     0
 ) '
2 x,-x,0 -1 {2-xy|0,0,0}'
27.y+1/2,-x,z+1/2
-my,mx,-mz
( 
  0   1   0   1/2
 -1   0   0     0
  0   0   1   1/2
 ) '
4- (0,0,1/2) 1/4,-1/4,z -1 {4z-1|1/2,0,1/2}'
28.-y,x+1/2,z+1/2
my,-mx,-mz
( 
  0  -1   0     0
  1   0   0   1/2
  0   0   1   1/2
 ) '
4+ (0,0,1/2) -1/4,1/4,z -1 {4z|0,1/2,1/2}'
29.x+1/2,z+1/2,-y
-mx,-mz,my
( 
  1   0   0   1/2
  0   0   1   1/2
  0  -1   0     0
 ) '
4- (1/2,0,0) x,1/4,-1/4 -1 {4x-1|1/2,1/2,0}'
30.-x,z+1/2,y+1/2
mx,-mz,-my
( 
 -1   0   0     0
  0   0   1   1/2
  0   1   0   1/2
 ) '
2 (0,1/2,1/2) 0,y,y -1 {2yz|0,1/2,1/2}'
31.-x,-z,-y
mx,mz,my
( 
 -1   0   0     0
  0   0  -1     0
  0  -1   0     0
 ) '
2 0,y,-y -1 {2-yz|0,0,0}'
32.x+1/2,-z,y+1/2
-mx,mz,-my
( 
  1   0   0   1/2
  0   0  -1     0
  0   1   0   1/2
 ) '
4+ (1/2,0,0) x,-1/4,1/4 -1 {4x|1/2,0,1/2}'
33.z+1/2,y+1/2,-x
-mz,-my,mx
( 
  0   0   1   1/2
  0   1   0   1/2
 -1   0   0     0
 ) '
4+ (0,1/2,0) 1/4,y,-1/4 -1 {4y|1/2,1/2,0}'
34.z+1/2,-y,x+1/2
-mz,my,-mx
( 
  0   0   1   1/2
  0  -1   0     0
  1   0   0   1/2
 ) '
2 (1/2,0,1/2) x,0,x -1 {2xz|1/2,0,1/2}'
35.-z,y+1/2,x+1/2
mz,-my,-mx
( 
  0   0  -1     0
  0   1   0   1/2
  1   0   0   1/2
 ) '
4- (0,1/2,0) -1/4,y,1/4 -1 {4y-1|0,1/2,1/2}'
36.-z,-y,-x
mz,my,mx
( 
  0   0  -1     0
  0  -1   0     0
 -1   0   0     0
 ) '
2 -x,0,x -1 {2-xz|0,0,0}'
37.-y+1/2,-x+1/2,z
-my,-mx,mz
( 
  0  -1   0   1/2
 -1   0   0   1/2
  0   0   1     0
 ) '
m x+1/2,-x,z -1 {mxy|1/2,1/2,0}'
38.y,x,z
my,mx,mz
( 
  0   1   0     0
  1   0   0     0
  0   0   1     0
 ) '
m x,x,z -1 {m-xy|0,0,0}'
39.-y+1/2,x,-z+1/2
-my,mx,-mz
( 
  0  -1   0   1/2
  1   0   0     0
  0   0  -1   1/2
 ) '
-4- 1/4,1/4,z 1/4,1/4,1/4 -1 {-4z-1|1/2,0,1/2}'
40.y,-x+1/2,-z+1/2
my,-mx,-mz
( 
  0   1   0     0
 -1   0   0   1/2
  0   0  -1   1/2
 ) '
-4+ 1/4,1/4,z 1/4,1/4,1/4 -1 {-4z|0,1/2,1/2}'
41.-x+1/2,-z+1/2,y
-mx,-mz,my
( 
 -1   0   0   1/2
  0   0  -1   1/2
  0   1   0     0
 ) '
-4- x,1/4,1/4 1/4,1/4,1/4 -1 {-4x-1|1/2,1/2,0}'
42.x,-z+1/2,-y+1/2
mx,-mz,-my
( 
  1   0   0     0
  0   0  -1   1/2
  0  -1   0   1/2
 ) '
m x,y+1/2,-y -1 {myz|0,1/2,1/2}'
43.x,z,y
mx,mz,my
( 
  1   0   0     0
  0   0   1     0
  0   1   0     0
 ) '
m x,y,y -1 {m-yz|0,0,0}'
44.-x+1/2,z,-y+1/2
-mx,mz,-my
( 
 -1   0   0   1/2
  0   0   1     0
  0  -1   0   1/2
 ) '
-4+ x,1/4,1/4 1/4,1/4,1/4 -1 {-4x|1/2,0,1/2}'
45.-z+1/2,-y+1/2,x
-mz,-my,mx
( 
  0   0  -1   1/2
  0  -1   0   1/2
  1   0   0     0
 ) '
-4+ 1/4,y,1/4 1/4,1/4,1/4 -1 {-4y|1/2,1/2,0}'
46.-z+1/2,y,-x+1/2
-mz,my,-mx
( 
  0   0  -1   1/2
  0   1   0     0
 -1   0   0   1/2
 ) '
m -x+1/2,y,x -1 {mxz|1/2,0,1/2}'
47.z,-y+1/2,-x+1/2
mz,-my,-mx
( 
  0   0   1     0
  0  -1   0   1/2
 -1   0   0   1/2
 ) '
-4- 1/4,y,1/4 1/4,1/4,1/4 -1 {-4y-1|0,1/2,1/2}'
48.z,y,x
mz,my,mx
( 
  0   0   1     0
  0   1   0     0
  1   0   0     0
 ) '
m x,y,x -1 {m-xz|0,0,0}'


Go to the Wyckoff Positions of 224.113 (Pn-3m')
Go to the extinction rules of 224.113 (Pn-3m')


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

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