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R-3'm' [#166.100] (Type: 3 -- Type III (translationgleiche))

[OG: R-3'm' #166.4.1330]

Operators of Group 166.100 (R-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.-y,x-y,z
-my,mx-my,mz
( 
  0  -1   0     0
  1  -1   0     0
  0   0   1     0
 )
3+ 0,0,z +1 {3z|0,0,0}
3.-x+y,-x,z
-mx+my,-mx,mz
( 
 -1   1   0     0
 -1   0   0     0
  0   0   1     0
 )
3- 0,0,z +1 {3z-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 {2xy|0,0,0}
5.x-y,-y,-z
mx-my,-my,-mz
( 
  1  -1   0     0
  0  -1   0     0
  0   0  -1     0
 )
2 x,0,0 +1 {2x|0,0,0}
6.-x,-x+y,-z
-mx,-mx+my,-mz
( 
 -1   0   0     0
 -1   1   0     0
  0   0  -1     0
 )
2 0,y,0 +1 {2y|0,0,0}
7.x+2/3,y+1/3,z+1/3
mx,my,mz
( 
  1   0   0   2/3
  0   1   0   1/3
  0   0   1   1/3
 )
t (2/3,1/3,1/3) +1 {1|2/3,1/3,1/3}
8d.-y+2/3,x-y+1/3,z+1/3
-my,mx-my,mz
( 
  0  -1   0   2/3
  1  -1   0   1/3
  0   0   1   1/3
 )
3+ (0,0,1/3) 1/3,1/3,z +1 {3z|2/3,1/3,1/3}
9d.-x+y+2/3,-x+1/3,z+1/3
-mx+my,-mx,mz
( 
 -1   1   0   2/3
 -1   0   0   1/3
  0   0   1   1/3
 )
3- (0,0,1/3) 1/3,0,z +1 {3z-1|2/3,1/3,1/3}
10d.y+2/3,x+1/3,-z+1/3
my,mx,-mz
( 
  0   1   0   2/3
  1   0   0   1/3
  0   0  -1   1/3
 )
2 (1/2,1/2,0) x,x-0.16668,1/6 +1 {2xy|2/3,1/3,1/3}
11d.x-y+2/3,-y+1/3,-z+1/3
mx-my,-my,-mz
( 
  1  -1   0   2/3
  0  -1   0   1/3
  0   0  -1   1/3
 )
2 (1/2,0,0) x,1/6,1/6 +1 {2x|2/3,1/3,1/3}
12d.-x+2/3,-x+y+1/3,-z+1/3
-mx,-mx+my,-mz
( 
 -1   0   0   2/3
 -1   1   0   1/3
  0   0  -1   1/3
 )
2 1/3,y,1/6 +1 {2y|2/3,1/3,1/3}
13.x+1/3,y+2/3,z+2/3
mx,my,mz
( 
  1   0   0   1/3
  0   1   0   2/3
  0   0   1   2/3
 )
t (1/3,2/3,2/3) +1 {1|1/3,2/3,2/3}
14d.-y+1/3,x-y+2/3,z+2/3
-my,mx-my,mz
( 
  0  -1   0   1/3
  1  -1   0   2/3
  0   0   1   2/3
 )
3+ (0,0,2/3) 0,1/3,z +1 {3z|1/3,2/3,2/3}
15d.-x+y+1/3,-x+2/3,z+2/3
-mx+my,-mx,mz
( 
 -1   1   0   1/3
 -1   0   0   2/3
  0   0   1   2/3
 )
3- (0,0,2/3) 1/3,1/3,z +1 {3z-1|1/3,2/3,2/3}
16d.y+1/3,x+2/3,-z+2/3
my,mx,-mz
( 
  0   1   0   1/3
  1   0   0   2/3
  0   0  -1   2/3
 )
2 (1/2,1/2,0) x,x+0.16668,1/3 +1 {2xy|1/3,2/3,2/3}
17d.x-y+1/3,-y+2/3,-z+2/3
mx-my,-my,-mz
( 
  1  -1   0   1/3
  0  -1   0   2/3
  0   0  -1   2/3
 )
2 x,1/3,1/3 +1 {2x|1/3,2/3,2/3}
18d.-x+1/3,-x+y+2/3,-z+2/3
-mx,-mx+my,-mz
( 
 -1   0   0   1/3
 -1   1   0   2/3
  0   0  -1   2/3
 )
2 (0,1/2,0) 1/6,y,1/3 +1 {2y|1/3,2/3,2/3}
19.-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}'
20.y,-x+y,-z
my,-mx+my,-mz
( 
  0   1   0     0
 -1   1   0     0
  0   0  -1     0
 ) '
-3+ 0,0,z 0,0,0 -1 {-3z|0,0,0}'
21.x-y,x,-z
mx-my,mx,-mz
( 
  1  -1   0     0
  1   0   0     0
  0   0  -1     0
 ) '
-3- 0,0,z 0,0,0 -1 {-3z-1|0,0,0}'
22.-y,-x,z
-my,-mx,mz
( 
  0  -1   0     0
 -1   0   0     0
  0   0   1     0
 ) '
m x,-x,z -1 {mxy|0,0,0}'
23.-x+y,y,z
-mx+my,my,mz
( 
 -1   1   0     0
  0   1   0     0
  0   0   1     0
 ) '
m x,2x,z -1 {mx|0,0,0}'
24.x,x-y,z
mx,mx-my,mz
( 
  1   0   0     0
  1  -1   0     0
  0   0   1     0
 ) '
m 2x,x,z -1 {my|0,0,0}'
25d.-x+2/3,-y+1/3,-z+1/3
-mx,-my,-mz
( 
 -1   0   0   2/3
  0  -1   0   1/3
  0   0  -1   1/3
 ) '
-1 1/3,1/6,1/6 -1 {-1|2/3,1/3,1/3}'
26d.y+2/3,-x+y+1/3,-z+1/3
my,-mx+my,-mz
( 
  0   1   0   2/3
 -1   1   0   1/3
  0   0  -1   1/3
 ) '
-3+ 1/3,-1/3,z 1/3,-1/3,1/6 -1 {-3z|2/3,1/3,1/3}'
27d.x-y+2/3,x+1/3,-z+1/3
mx-my,mx,-mz
( 
  1  -1   0   2/3
  1   0   0   1/3
  0   0  -1   1/3
 ) '
-3- 1/3,2/3,z 1/3,2/3,1/6 -1 {-3z-1|2/3,1/3,1/3}'
28d.-y+2/3,-x+1/3,z+1/3
-my,-mx,mz
( 
  0  -1   0   2/3
 -1   0   0   1/3
  0   0   1   1/3
 ) '
g (1/6,-1/6,1/3) x+1/2,-x,z -1 {mxy|2/3,1/3,1/3}'
29d.-x+y+2/3,y+1/3,z+1/3
-mx+my,my,mz
( 
 -1   1   0   2/3
  0   1   0   1/3
  0   0   1   1/3
 ) '
g (1/6,1/3,1/3) x+1/4,2x,z -1 {mx|2/3,1/3,1/3}'
30d.x+2/3,x-y+1/3,z+1/3
mx,mx-my,mz
( 
  1   0   0   2/3
  1  -1   0   1/3
  0   0   1   1/3
 ) '
g (2/3,1/3,1/3) 2x,x,z -1 {my|2/3,1/3,1/3}'
31d.-x+1/3,-y+2/3,-z+2/3
-mx,-my,-mz
( 
 -1   0   0   1/3
  0  -1   0   2/3
  0   0  -1   2/3
 ) '
-1 1/6,1/3,1/3 -1 {-1|1/3,2/3,2/3}'
32d.y+1/3,-x+y+2/3,-z+2/3
my,-mx+my,-mz
( 
  0   1   0   1/3
 -1   1   0   2/3
  0   0  -1   2/3
 ) '
-3+ 2/3,1/3,z 2/3,1/3,1/3 -1 {-3z|1/3,2/3,2/3}'
33d.x-y+1/3,x+2/3,-z+2/3
mx-my,mx,-mz
( 
  1  -1   0   1/3
  1   0   0   2/3
  0   0  -1   2/3
 ) '
-3- -1/3,1/3,z -1/3,1/3,1/3 -1 {-3z-1|1/3,2/3,2/3}'
34d.-y+1/3,-x+2/3,z+2/3
-my,-mx,mz
( 
  0  -1   0   1/3
 -1   0   0   2/3
  0   0   1   2/3
 ) '
g (-1/6,1/6,2/3) x+1/2,-x,z -1 {mxy|1/3,2/3,2/3}'
35d.-x+y+1/3,y+2/3,z+2/3
-mx+my,my,mz
( 
 -1   1   0   1/3
  0   1   0   2/3
  0   0   1   2/3
 ) '
g (1/3,2/3,2/3) x,2x,z -1 {mx|1/3,2/3,2/3}'
36d.x+1/3,x-y+2/3,z+2/3
mx,mx-my,mz
( 
  1   0   0   1/3
  1  -1   0   2/3
  0   0   1   2/3
 ) '
g (1/3,1/6,2/3) 2x-0.5,x,z -1 {my|1/3,2/3,2/3}'
Show/Hide Derived operators due to the centring translations


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