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Fd'-3'm' [#227.132] (Type: 3 -- Type III (translationgleiche))

[OG: Fd'-3'm' #227.5.1632]

Operators of Group 227.132 (Fd'-3'm')

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.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}
3.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}
4.-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}
5.-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}
6.-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}
7.x,y+1/2,z+1/2
mx,my,mz
( 
  1   0   0     0
  0   1   0   1/2
  0   0   1   1/2
 )
t (0,1/2,1/2) +1 {1|0,1/2,1/2}
8.-x+1/4,y,-z+1/4
-mx,my,-mz
( 
 -1   0   0   1/4
  0   1   0     0
  0   0  -1   1/4
 )
2 1/8,y,1/8 +1 {2y|1/4,0,1/4}
9.-z+1/4,x,-y+1/4
-mz,mx,-my
( 
  0   0  -1   1/4
  1   0   0     0
  0  -1   0   1/4
 )
3+ -x+1/4,-x+1/4,x +1 {3xy-z-1|1/4,0,1/4}
10.-y+1/4,z,-x+1/4
-my,mz,-mx
( 
  0  -1   0   1/4
  0   0   1     0
 -1   0   0   1/4
 )
3- x+1/4,-x,-x +1 {3-xyz|1/4,0,1/4}
11.y+1/4,-x,z+1/4
my,-mx,mz
( 
  0   1   0   1/4
 -1   0   0     0
  0   0   1   1/4
 )
4- (0,0,1/4) 1/8,-1/8,z +1 {4z-1|1/4,0,1/4}
12.x+1/4,-z,y+1/4
mx,-mz,my
( 
  1   0   0   1/4
  0   0  -1     0
  0   1   0   1/4
 )
4+ (1/4,0,0) x,-1/8,1/8 +1 {4x|1/4,0,1/4}
13.z+1/4,-y,x+1/4
mz,-my,mx
( 
  0   0   1   1/4
  0  -1   0     0
  1   0   0   1/4
 )
2 (1/4,0,1/4) x,0,x +1 {2xz|1/4,0,1/4}
14.x+1/2,y,z+1/2
mx,my,mz
( 
  1   0   0   1/2
  0   1   0     0
  0   0   1   1/2
 )
t (1/2,0,1/2) +1 {1|1/2,0,1/2}
15.-x+1/4,-y+1/4,z
-mx,-my,mz
( 
 -1   0   0   1/4
  0  -1   0   1/4
  0   0   1     0
 )
2 1/8,1/8,z +1 {2z|1/4,1/4,0}
16.-z+1/4,-x+1/4,y
-mz,-mx,my
( 
  0   0  -1   1/4
 -1   0   0   1/4
  0   1   0     0
 )
3+ x+1/4,-x,-x +1 {3-xyz-1|1/4,1/4,0}
17.-y+1/4,-z+1/4,x
-my,-mz,mx
( 
  0  -1   0   1/4
  0   0  -1   1/4
  1   0   0     0
 )
3- -x,x+1/4,-x +1 {3x-yz|1/4,1/4,0}
18.y+1/4,x+1/4,-z
my,mx,-mz
( 
  0   1   0   1/4
  1   0   0   1/4
  0   0  -1     0
 )
2 (1/4,1/4,0) x,x,0 +1 {2xy|1/4,1/4,0}
19.x+1/4,z+1/4,-y
mx,mz,-my
( 
  1   0   0   1/4
  0   0   1   1/4
  0  -1   0     0
 )
4- (1/4,0,0) x,1/8,-1/8 +1 {4x-1|1/4,1/4,0}
20.z+1/4,y+1/4,-x
mz,my,-mx
( 
  0   0   1   1/4
  0   1   0   1/4
 -1   0   0     0
 )
4+ (0,1/4,0) 1/8,y,-1/8 +1 {4y|1/4,1/4,0}
21.x+1/2,y+1/2,z
mx,my,mz
( 
  1   0   0   1/2
  0   1   0   1/2
  0   0   1     0
 )
t (1/2,1/2,0) +1 {1|1/2,1/2,0}
22.x,-y+1/4,-z+1/4
mx,-my,-mz
( 
  1   0   0     0
  0  -1   0   1/4
  0   0  -1   1/4
 )
2 x,1/8,1/8 +1 {2x|0,1/4,1/4}
23.z,-x+1/4,-y+1/4
mz,-mx,-my
( 
  0   0   1     0
 -1   0   0   1/4
  0  -1   0   1/4
 )
3+ -x,x+1/4,-x +1 {3x-yz-1|0,1/4,1/4}
24.y,-z+1/4,-x+1/4
my,-mz,-mx
( 
  0   1   0     0
  0   0  -1   1/4
 -1   0   0   1/4
 )
3- -x+1/4,-x+1/4,x +1 {3xy-z|0,1/4,1/4}
25.-y,x+1/4,z+1/4
-my,mx,mz
( 
  0  -1   0     0
  1   0   0   1/4
  0   0   1   1/4
 )
4+ (0,0,1/4) -1/8,1/8,z +1 {4z|0,1/4,1/4}
26.-x,z+1/4,y+1/4
-mx,mz,my
( 
 -1   0   0     0
  0   0   1   1/4
  0   1   0   1/4
 )
2 (0,1/4,1/4) 0,y,y +1 {2yz|0,1/4,1/4}
27.-z,y+1/4,x+1/4
-mz,my,mx
( 
  0   0  -1     0
  0   1   0   1/4
  1   0   0   1/4
 )
4- (0,1/4,0) -1/8,y,1/8 +1 {4y-1|0,1/4,1/4}
28.-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}'
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.-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}'
31.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}'
32.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}'
33.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}'
34.x+1/4,y+1/4,-z
mx,my,-mz
( 
  1   0   0   1/4
  0   1   0   1/4
  0   0  -1     0
 ) '
d (1/4,1/4,0) x,y,0 -1 {mz|1/4,1/4,0}'
35.z+1/4,x+1/4,-y
mz,mx,-my
( 
  0   0   1   1/4
  1   0   0   1/4
  0  -1   0     0
 ) '
-3+ x-0.25,-x+1/2,-x 0,1/4,-1/4 -1 {-3-xyz-1|1/4,1/4,0}'
36.y+1/4,z+1/4,-x
my,mz,-mx
( 
  0   1   0   1/4
  0   0   1   1/4
 -1   0   0     0
 ) '
-3- -x+1/2,x-1/4,-x 1/4,0,-1/4 -1 {-3x-yz|1/4,1/4,0}'
37.-y+1/4,-x+1/4,z
-my,-mx,mz
( 
  0  -1   0   1/4
 -1   0   0   1/4
  0   0   1     0
 ) '
m x+1/4,-x,z -1 {mxy|1/4,1/4,0}'
38.-x+1/4,-z+1/4,y
-mx,-mz,my
( 
 -1   0   0   1/4
  0   0  -1   1/4
  0   1   0     0
 ) '
-4- x,1/8,1/8 1/8,1/8,1/8 -1 {-4x-1|1/4,1/4,0}'
39.-z+1/4,-y+1/4,x
-mz,-my,mx
( 
  0   0  -1   1/4
  0  -1   0   1/4
  1   0   0     0
 ) '
-4+ 1/8,y,1/8 1/8,1/8,1/8 -1 {-4y|1/4,1/4,0}'
40.-x,y+1/4,z+1/4
-mx,my,mz
( 
 -1   0   0     0
  0   1   0   1/4
  0   0   1   1/4
 ) '
d (0,1/4,1/4) 0,y,z -1 {mx|0,1/4,1/4}'
41.-z,x+1/4,y+1/4
-mz,mx,my
( 
  0   0  -1     0
  1   0   0   1/4
  0   1   0   1/4
 ) '
-3+ -x-1/2,x+1/4,-x -1/4,0,1/4 -1 {-3x-yz-1|0,1/4,1/4}'
42.-y,z+1/4,x+1/4
-my,mz,mx
( 
  0  -1   0     0
  0   0   1   1/4
  1   0   0   1/4
 ) '
-3- -x-1/4,-x+1/4,x -1/4,1/4,0 -1 {-3xy-z|0,1/4,1/4}'
43.y,-x+1/4,-z+1/4
my,-mx,-mz
( 
  0   1   0     0
 -1   0   0   1/4
  0   0  -1   1/4
 ) '
-4+ 1/8,1/8,z 1/8,1/8,1/8 -1 {-4z|0,1/4,1/4}'
44.x,-z+1/4,-y+1/4
mx,-mz,-my
( 
  1   0   0     0
  0   0  -1   1/4
  0  -1   0   1/4
 ) '
m x,y+1/4,-y -1 {myz|0,1/4,1/4}'
45.z,-y+1/4,-x+1/4
mz,-my,-mx
( 
  0   0   1     0
  0  -1   0   1/4
 -1   0   0   1/4
 ) '
-4- 1/8,y,1/8 1/8,1/8,1/8 -1 {-4y-1|0,1/4,1/4}'
46.x+1/4,-y,z+1/4
mx,-my,mz
( 
  1   0   0   1/4
  0  -1   0     0
  0   0   1   1/4
 ) '
d (1/4,0,1/4) x,0,z -1 {my|1/4,0,1/4}'
47.z+1/4,-x,y+1/4
mz,-mx,my
( 
  0   0   1   1/4
 -1   0   0     0
  0   1   0   1/4
 ) '
-3+ -x+1/4,-x,x 1/4,-1/4,0 -1 {-3xy-z-1|1/4,0,1/4}'
48.y+1/4,-z,x+1/4
my,-mz,mx
( 
  0   1   0   1/4
  0   0  -1     0
  1   0   0   1/4
 ) '
-3- x+1/4,-x,-x 0,-1/4,1/4 -1 {-3-xyz|1/4,0,1/4}'
49.-y+1/4,x,-z+1/4
-my,mx,-mz
( 
  0  -1   0   1/4
  1   0   0     0
  0   0  -1   1/4
 ) '
-4- 1/8,1/8,z 1/8,1/8,1/8 -1 {-4z-1|1/4,0,1/4}'
50.-x+1/4,z,-y+1/4
-mx,mz,-my
( 
 -1   0   0   1/4
  0   0   1     0
  0  -1   0   1/4
 ) '
-4+ x,1/8,1/8 1/8,1/8,1/8 -1 {-4x|1/4,0,1/4}'
51.-z+1/4,y,-x+1/4
-mz,my,-mx
( 
  0   0  -1   1/4
  0   1   0     0
 -1   0   0   1/4
 ) '
m -x+1/4,y,x -1 {mxz|1/4,0,1/4}'
Show/Hide Derived operators due to the centring translations


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