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Im'-3' [#204.32] (Type: 3 -- Type III (translationgleiche))

[OG: Im'-3' #204.3.1532]

Operators of Group 204.32 (Im'-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,-y,z
-mx,-my,mz
( 
 -1   0   0     0
  0  -1   0     0
  0   0   1     0
 )
2 0,0,z +1 {2z|0,0,0}
3.-x,y,-z
-mx,my,-mz
( 
 -1   0   0     0
  0   1   0     0
  0   0  -1     0
 )
2 0,y,0 +1 {2y|0,0,0}
4.x,-y,-z
mx,-my,-mz
( 
  1   0   0     0
  0  -1   0     0
  0   0  -1     0
 )
2 x,0,0 +1 {2x|0,0,0}
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,-y
mz,-mx,-my
( 
  0   0   1     0
 -1   0   0     0
  0  -1   0     0
 )
3+ -x,x,-x +1 {3x-yz-1|0,0,0}
7.-z,-x,y
-mz,-mx,my
( 
  0   0  -1     0
 -1   0   0     0
  0   1   0     0
 )
3+ x,-x,-x +1 {3-xyz-1|0,0,0}
8.-z,x,-y
-mz,mx,-my
( 
  0   0  -1     0
  1   0   0     0
  0  -1   0     0
 )
3+ -x,-x,x +1 {3xy-z-1|0,0,0}
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,z,-x
-my,mz,-mx
( 
  0  -1   0     0
  0   0   1     0
 -1   0   0     0
 )
3- x,-x,-x +1 {3-xyz|0,0,0}
11.y,-z,-x
my,-mz,-mx
( 
  0   1   0     0
  0   0  -1     0
 -1   0   0     0
 )
3- -x,-x,x +1 {3xy-z|0,0,0}
12.-y,-z,x
-my,-mz,mx
( 
  0  -1   0     0
  0   0  -1     0
  1   0   0     0
 )
3- -x,x,-x +1 {3x-yz|0,0,0}
13.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}
14d.-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
 )
2 (0,0,1/2) 1/4,1/4,z +1 {2z|1/2,1/2,1/2}
15d.-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
 )
2 (0,1/2,0) 1/4,y,1/4 +1 {2y|1/2,1/2,1/2}
16d.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
 )
2 (1/2,0,0) x,1/4,1/4 +1 {2x|1/2,1/2,1/2}
17d.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}
18d.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+ (1/6,-1/6,1/6) -x+1/3,x+1/3,-x +1 {3x-yz-1|1/2,1/2,1/2}
19d.-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+ (-1/6,1/6,1/6) x+2/3,-x,-x +1 {3-xyz-1|1/2,1/2,1/2}
20d.-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+ (1/6,1/6,-1/6) -x+1/3,-x+2/3,x +1 {3xy-z-1|1/2,1/2,1/2}
21d.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}
22d.-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- (-1/6,1/6,1/6) x+1/3,-x+1/3,-x +1 {3-xyz|1/2,1/2,1/2}
23d.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- (1/6,1/6,-1/6) -x+2/3,-x+1/3,x +1 {3xy-z|1/2,1/2,1/2}
24d.-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- (1/6,-1/6,1/6) -x-1/3,x+2/3,-x +1 {3x-yz|1/2,1/2,1/2}
25.-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}'
26.x,y,-z
mx,my,-mz
( 
  1   0   0     0
  0   1   0     0
  0   0  -1     0
 ) '
m x,y,0 -1 {mz|0,0,0}'
27.x,-y,z
mx,-my,mz
( 
  1   0   0     0
  0  -1   0     0
  0   0   1     0
 ) '
m x,0,z -1 {my|0,0,0}'
28.-x,y,z
-mx,my,mz
( 
 -1   0   0     0
  0   1   0     0
  0   0   1     0
 ) '
m 0,y,z -1 {mx|0,0,0}'
29.-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}'
30.-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 {-3x-yz-1|0,0,0}'
31.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 {-3-xyz-1|0,0,0}'
32.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 {-3xy-z-1|0,0,0}'
33.-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}'
34.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 {-3-xyz|0,0,0}'
35.-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 {-3xy-z|0,0,0}'
36.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 {-3x-yz|0,0,0}'
37d.-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}'
38d.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
 ) '
n (1/2,1/2,0) x,y,1/4 -1 {mz|1/2,1/2,1/2}'
39d.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
 ) '
n (1/2,0,1/2) x,1/4,z -1 {my|1/2,1/2,1/2}'
40d.-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
 ) '
n (0,1/2,1/2) 1/4,y,z -1 {mx|1/2,1/2,1/2}'
41d.-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}'
42d.-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-1,x+1,-x -1/4,1/4,3/4 -1 {-3x-yz-1|1/2,1/2,1/2}'
43d.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+1,-x 1/4,3/4,-1/4 -1 {-3-xyz-1|1/2,1/2,1/2}'
44d.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+1,-x,x 3/4,-1/4,1/4 -1 {-3xy-z-1|1/2,1/2,1/2}'
45d.-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}'
46d.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+1,-x,-x 1/4,-1/4,3/4 -1 {-3-xyz|1/2,1/2,1/2}'
47d.-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+1,x -1/4,3/4,1/4 -1 {-3xy-z|1/2,1/2,1/2}'
48d.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+1,x,-x 3/4,1/4,-1/4 -1 {-3x-yz|1/2,1/2,1/2}'
Show/Hide Derived operators due to the centring translations


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