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I-4'3d' [#220.91] (Type: 3 -- Type III (translationgleiche))

[OG: I-4'3d' #220.3.1593]

Operators of Group 220.91 (I-4'3d')

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


Go to the Wyckoff Positions of 220.91 (I-4'3d')
Go to the extinction rules of 220.91 (I-4'3d')


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