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Ia'-3'd' [#230.149] (Type: 3 -- Type III (translationgleiche))

[OG: Ia'-3'd' #230.5.1651]

Operators of Group 230.149 (Ia'-3'd')

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+3/4,x+1/4,-z+1/4
my,mx,-mz
( 
  0   1   0   3/4
  1   0   0   1/4
  0   0  -1   1/4
 )
2 (1/2,1/2,0) x,x-1/4,1/8 +1 {2xy|3/4,1/4,1/4}
5.y+1/4,-x+1/4,z+3/4
my,-mx,mz
( 
  0   1   0   1/4
 -1   0   0   1/4
  0   0   1   3/4
 )
4- (0,0,3/4) 1/4,0,z +1 {4z-1|1/4,1/4,3/4}
6.-y+1/4,x+3/4,z+1/4
-my,mx,mz
( 
  0  -1   0   1/4
  1   0   0   3/4
  0   0   1   1/4
 )
4+ (0,0,1/4) -1/4,1/2,z +1 {4z|1/4,3/4,1/4}
7.x+3/4,z+1/4,-y+1/4
mx,mz,-my
( 
  1   0   0   3/4
  0   0   1   1/4
  0  -1   0   1/4
 )
4- (3/4,0,0) x,1/4,0 +1 {4x-1|3/4,1/4,1/4}
8.-x+1/4,z+3/4,y+1/4
-mx,mz,my
( 
 -1   0   0   1/4
  0   0   1   3/4
  0   1   0   1/4
 )
2 (0,1/2,1/2) 1/8,y+1/4,y +1 {2yz|1/4,3/4,1/4}
9.x+1/4,-z+1/4,y+3/4
mx,-mz,my
( 
  1   0   0   1/4
  0   0  -1   1/4
  0   1   0   3/4
 )
4+ (1/4,0,0) x,-1/4,1/2 +1 {4x|1/4,1/4,3/4}
10.z+3/4,y+1/4,-x+1/4
mz,my,-mx
( 
  0   0   1   3/4
  0   1   0   1/4
 -1   0   0   1/4
 )
4+ (0,1/4,0) 1/2,y,-1/4 +1 {4y|3/4,1/4,1/4}
11.z+1/4,-y+1/4,x+3/4
mz,-my,mx
( 
  0   0   1   1/4
  0  -1   0   1/4
  1   0   0   3/4
 )
2 (1/2,0,1/2) x-0.25,1/8,x +1 {2xz|1/4,1/4,3/4}
12.-z+1/4,y+3/4,x+1/4
-mz,my,mx
( 
  0   0  -1   1/4
  0   1   0   3/4
  1   0   0   1/4
 )
4- (0,3/4,0) 0,y,1/4 +1 {4y-1|1/4,3/4,1/4}
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}
14.-x,-y+1/2,z
-mx,-my,mz
( 
 -1   0   0     0
  0  -1   0   1/2
  0   0   1     0
 )
2 0,1/4,z +1 {2z|0,1/2,0}
15.-x+1/2,y,-z
-mx,my,-mz
( 
 -1   0   0   1/2
  0   1   0     0
  0   0  -1     0
 )
2 1/4,y,0 +1 {2y|1/2,0,0}
16.x,-y,-z+1/2
mx,-my,-mz
( 
  1   0   0     0
  0  -1   0     0
  0   0  -1   1/2
 )
2 x,0,1/4 +1 {2x|0,0,1/2}
17.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+1/3,-x +1 {3x-yz-1|0,0,1/2}
18.-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 {3-xyz-1|0,1/2,0}
19.-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 {3xy-z-1|1/2,0,0}
20.-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+1/6,-x +1 {3-xyz|1/2,0,0}
21.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 {3xy-z|0,0,1/2}
22.-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-1/6,x+1/3,-x +1 {3x-yz|0,1/2,0}
23.-y+1/4,-x+1/4,-z+1/4
-my,-mx,-mz
( 
  0  -1   0   1/4
 -1   0   0   1/4
  0   0  -1   1/4
 )
2 x,-x+1/4,1/8 +1 {2-xy|1/4,1/4,1/4}
24.-x+1/4,-z+1/4,-y+1/4
-mx,-mz,-my
( 
 -1   0   0   1/4
  0   0  -1   1/4
  0  -1   0   1/4
 )
2 1/8,y+1/4,-y +1 {2-yz|1/4,1/4,1/4}
25.-z+1/4,-y+1/4,-x+1/4
-mz,-my,-mx
( 
  0   0  -1   1/4
  0  -1   0   1/4
 -1   0   0   1/4
 )
2 -x+1/4,1/8,x +1 {2-xz|1/4,1/4,1/4}
26.-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}'
27.-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}'
28.-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}'
29.y+1/4,x+1/4,z+1/4
my,mx,mz
( 
  0   1   0   1/4
  1   0   0   1/4
  0   0   1   1/4
 ) '
d (1/4,1/4,1/4) x,x,z -1 {m-xy|1/4,1/4,1/4}'
30.x+1/4,z+1/4,y+1/4
mx,mz,my
( 
  1   0   0   1/4
  0   0   1   1/4
  0   1   0   1/4
 ) '
d (1/4,1/4,1/4) x,y,y -1 {m-yz|1/4,1/4,1/4}'
31.z+1/4,y+1/4,x+1/4
mz,my,mx
( 
  0   0   1   1/4
  0   1   0   1/4
  1   0   0   1/4
 ) '
d (1/4,1/4,1/4) x,y,x -1 {m-xz|1/4,1/4,1/4}'
32.x,y+1/2,-z
mx,my,-mz
( 
  1   0   0     0
  0   1   0   1/2
  0   0  -1     0
 ) '
b x,y,0 -1 {mz|0,1/2,0}'
33.x+1/2,-y,z
mx,-my,mz
( 
  1   0   0   1/2
  0  -1   0     0
  0   0   1     0
 ) '
a x,0,z -1 {my|1/2,0,0}'
34.-x,y,z+1/2
-mx,my,mz
( 
 -1   0   0     0
  0   1   0     0
  0   0   1   1/2
 ) '
c 0,y,z -1 {mx|0,0,1/2}'
35.-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 {-3x-yz-1|0,0,1/2}'
36.z,x+1/2,-y
mz,mx,-my
( 
  0   0   1     0
  1   0   0   1/2
  0  -1   0     0
 ) '
-3+ x-0.5,-x+1/2,-x -1/4,1/4,-1/4 -1 {-3-xyz-1|0,1/2,0}'
37.z+1/2,-x,y
mz,-mx,my
( 
  0   0   1   1/2
 -1   0   0     0
  0   1   0     0
 ) '
-3+ -x,-x,x 1/4,-1/4,-1/4 -1 {-3xy-z-1|1/2,0,0}'
38.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,-x 1/4,-1/4,1/4 -1 {-3-xyz|1/2,0,0}'
39.-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 {-3xy-z|0,0,1/2}'
40.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 {-3x-yz|0,1/2,0}'
41.-y+3/4,-x+1/4,z+1/4
-my,-mx,mz
( 
  0  -1   0   3/4
 -1   0   0   1/4
  0   0   1   1/4
 ) '
d (1/4,-1/4,1/4) x+1/2,-x,z -1 {mxy|3/4,1/4,1/4}'
42.-y+1/4,x+1/4,-z+3/4
-my,mx,-mz
( 
  0  -1   0   1/4
  1   0   0   1/4
  0   0  -1   3/4
 ) '
-4- 0,1/4,z 0,1/4,3/8 -1 {-4z-1|1/4,1/4,3/4}'
43.y+1/4,-x+3/4,-z+1/4
my,-mx,-mz
( 
  0   1   0   1/4
 -1   0   0   3/4
  0   0  -1   1/4
 ) '
-4+ 1/2,1/4,z 1/2,1/4,1/8 -1 {-4z|1/4,3/4,1/4}'
44.-x+3/4,-z+1/4,y+1/4
-mx,-mz,my
( 
 -1   0   0   3/4
  0   0  -1   1/4
  0   1   0   1/4
 ) '
-4- x,0,1/4 3/8,0,1/4 -1 {-4x-1|3/4,1/4,1/4}'
45.x+1/4,-z+3/4,-y+1/4
mx,-mz,-my
( 
  1   0   0   1/4
  0   0  -1   3/4
  0  -1   0   1/4
 ) '
d (1/4,1/4,-1/4) x,y+1/2,-y -1 {myz|1/4,3/4,1/4}'
46.-x+1/4,z+1/4,-y+3/4
-mx,mz,-my
( 
 -1   0   0   1/4
  0   0   1   1/4
  0  -1   0   3/4
 ) '
-4+ x,1/2,1/4 1/8,1/2,1/4 -1 {-4x|1/4,1/4,3/4}'
47.-z+3/4,-y+1/4,x+1/4
-mz,-my,mx
( 
  0   0  -1   3/4
  0  -1   0   1/4
  1   0   0   1/4
 ) '
-4+ 1/4,y,1/2 1/4,1/8,1/2 -1 {-4y|3/4,1/4,1/4}'
48.-z+1/4,y+1/4,-x+3/4
-mz,my,-mx
( 
  0   0  -1   1/4
  0   1   0   1/4
 -1   0   0   3/4
 ) '
d (-1/4,1/4,1/4) -x+1/2,y,x -1 {mxz|1/4,1/4,3/4}'
49.z+1/4,-y+3/4,-x+1/4
mz,-my,-mx
( 
  0   0   1   1/4
  0  -1   0   3/4
 -1   0   0   1/4
 ) '
-4- 1/4,y,0 1/4,3/8,0 -1 {-4y-1|1/4,3/4,1/4}'
Show/Hide Derived operators due to the centring translations


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