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I-4'3m' [#217.80] (Type: 3 -- Type III (translationgleiche))

[OG: I-4'3m' #217.3.1582]

Operators of Group 217.80 (I-4'3m')

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,-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.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}'
26.-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}'
27.y,-x,-z
my,-mx,-mz
( 
  0   1   0     0
 -1   0   0     0
  0   0  -1     0
 ) '
-4+ 0,0,z 0,0,0 -1 {-4z|0,0,0}'
28.-y,x,-z
-my,mx,-mz
( 
  0  -1   0     0
  1   0   0     0
  0   0  -1     0
 ) '
-4- 0,0,z 0,0,0 -1 {-4z-1|0,0,0}'
29.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}'
30.-x,z,-y
-mx,mz,-my
( 
 -1   0   0     0
  0   0   1     0
  0  -1   0     0
 ) '
-4+ x,0,0 0,0,0 -1 {-4x|0,0,0}'
31.-x,-z,y
-mx,-mz,my
( 
 -1   0   0     0
  0   0  -1     0
  0   1   0     0
 ) '
-4- x,0,0 0,0,0 -1 {-4x-1|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 {myz|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.z,-y,-x
mz,-my,-mx
( 
  0   0   1     0
  0  -1   0     0
 -1   0   0     0
 ) '
-4- 0,y,0 0,0,0 -1 {-4y-1|0,0,0}'
35.-z,y,-x
-mz,my,-mx
( 
  0   0  -1     0
  0   1   0     0
 -1   0   0     0
 ) '
m -x,y,x -1 {mxz|0,0,0}'
36.-z,-y,x
-mz,-my,mx
( 
  0   0  -1     0
  0  -1   0     0
  1   0   0     0
 ) '
-4+ 0,y,0 0,0,0 -1 {-4y|0,0,0}'
37d.y+1/2,x+1/2,z+1/2
my,mx,mz
( 
  0   1   0   1/2
  1   0   0   1/2
  0   0   1   1/2
 ) '
n (1/2,1/2,1/2) x,x,z -1 {m-xy|1/2,1/2,1/2}'
38d.-y+1/2,-x+1/2,z+1/2
-my,-mx,mz
( 
  0  -1   0   1/2
 -1   0   0   1/2
  0   0   1   1/2
 ) '
c x+1/2,-x,z -1 {mxy|1/2,1/2,1/2}'
39d.y+1/2,-x+1/2,-z+1/2
my,-mx,-mz
( 
  0   1   0   1/2
 -1   0   0   1/2
  0   0  -1   1/2
 ) '
-4+ 1/2,0,z 1/2,0,1/4 -1 {-4z|1/2,1/2,1/2}'
40d.-y+1/2,x+1/2,-z+1/2
-my,mx,-mz
( 
  0  -1   0   1/2
  1   0   0   1/2
  0   0  -1   1/2
 ) '
-4- 0,1/2,z 0,1/2,1/4 -1 {-4z-1|1/2,1/2,1/2}'
41d.x+1/2,z+1/2,y+1/2
mx,mz,my
( 
  1   0   0   1/2
  0   0   1   1/2
  0   1   0   1/2
 ) '
n (1/2,1/2,1/2) x,y,y -1 {m-yz|1/2,1/2,1/2}'
42d.-x+1/2,z+1/2,-y+1/2
-mx,mz,-my
( 
 -1   0   0   1/2
  0   0   1   1/2
  0  -1   0   1/2
 ) '
-4+ x,1/2,0 1/4,1/2,0 -1 {-4x|1/2,1/2,1/2}'
43d.-x+1/2,-z+1/2,y+1/2
-mx,-mz,my
( 
 -1   0   0   1/2
  0   0  -1   1/2
  0   1   0   1/2
 ) '
-4- x,0,1/2 1/4,0,1/2 -1 {-4x-1|1/2,1/2,1/2}'
44d.x+1/2,-z+1/2,-y+1/2
mx,-mz,-my
( 
  1   0   0   1/2
  0   0  -1   1/2
  0  -1   0   1/2
 ) '
a x,y+1/2,-y -1 {myz|1/2,1/2,1/2}'
45d.z+1/2,y+1/2,x+1/2
mz,my,mx
( 
  0   0   1   1/2
  0   1   0   1/2
  1   0   0   1/2
 ) '
n (1/2,1/2,1/2) x,y,x -1 {m-xz|1/2,1/2,1/2}'
46d.z+1/2,-y+1/2,-x+1/2
mz,-my,-mx
( 
  0   0   1   1/2
  0  -1   0   1/2
 -1   0   0   1/2
 ) '
-4- 1/2,y,0 1/2,1/4,0 -1 {-4y-1|1/2,1/2,1/2}'
47d.-z+1/2,y+1/2,-x+1/2
-mz,my,-mx
( 
  0   0  -1   1/2
  0   1   0   1/2
 -1   0   0   1/2
 ) '
b -x+1/2,y,x -1 {mxz|1/2,1/2,1/2}'
48d.-z+1/2,-y+1/2,x+1/2
-mz,-my,mx
( 
  0   0  -1   1/2
  0  -1   0   1/2
  1   0   0   1/2
 ) '
-4+ 0,y,1/2 0,1/4,1/2 -1 {-4y|1/2,1/2,1/2}'
Show/Hide Derived operators due to the centring translations


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