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IPa-3' [#206.4.1541] (Type: 4 -- Type IV (klassengleiche))

[BNS: PIa-3] #205.36

Operators of Group 206.4.1541 (IPa-3')

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+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}
3.-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}
4.-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}
5.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}
6.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}
7.-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}
8.-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}
9.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}
10.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}
11.-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}
12.-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}
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
 )
-1 1/4,1/4,1/4 +1 {-1|1/2,1/2,1/2}
14.-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}
15.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}
16.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}
17.-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- x,x,x; 1/4,1/4,1/4 +1 {-3xyz-1|1/2,1/2,1/2}
18.-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}
19.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}
20.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}
21.-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+ x,x,x; 1/4,1/4,1/4 +1 {-3xyz|1/2,1/2,1/2}
22.-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}
23.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}
24.z,x+1/2,-y
-mz,-mx,my
( 
  0   0   1     0
  1   0   0   1/2
  0  -1   0     0
 )
-3+ x-1/2,-x+1/2,-x; -1/4,1/4,-1/4 +1 {-3-xyz-1|0,1/2,0}
25.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}'
26.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}'
27.-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}'
28.-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}'
29.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}'
30.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}'
31.-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}'
32.-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}'
33.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}'
34.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}'
35.-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}'
36.-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}'
37.-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}'
38.-x+1/2,y+1/2,z
-mx,my,mz
( 
 -1   0   0   1/2
  0   1   0   1/2
  0   0   1     0
 ) '
b 1/4,y,z -1 {mx|1/2,1/2,0}'
39.x,-y+1/2,z+1/2
mx,-my,mz
( 
  1   0   0     0
  0  -1   0   1/2
  0   0   1   1/2
 ) '
c x,1/4,z -1 {my|0,1/2,1/2}'
40.x+1/2,y,-z+1/2
mx,my,-mz
( 
  1   0   0   1/2
  0   1   0     0
  0   0  -1   1/2
 ) '
a x,y,1/4 -1 {mz|1/2,0,1/2}'
41.-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}'
42.-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- -x,-x+1/2,x; 0,1/2,0 -1 {-3xy-z|1/2,1/2,0}'
43.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- x+1/2,-x,-x; 0,0,1/2 -1 {-3-xyz|0,1/2,1/2}'
44.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- -x+1/2,x,-x; 1/2,0,0 -1 {-3x-yz|1/2,0,1/2}'
45.-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}'
46.-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+1,-x; 0,1/2,1/2 -1 {-3x-yz-1|1/2,1/2,0}'
47.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+1,-x+1/2,x; 1/2,0,1/2 -1 {-3xy-z-1|0,1/2,1/2}'
48.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+1/2,-x; 1/2,1/2,0 -1 {-3-xyz-1|1/2,0,1/2}'


Go to the Wyckoff Positions of 206.4.1541 (IPa-3')
Go to the extinction rules of 205.36 (PIa-3) ← Corresponding space group in BNS settings


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