Bilbao Crystallographic Server arrow MGENPOS arrow Table of Magnetic Space Group Symbols Help

I41/a'c'd' [#142.569] (Type: 3 -- Type III (translationgleiche))

[OG: I41/a'c'd' #142.9.1230]

Operators of Group 142.569 (I41/a'c'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}
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}
3.-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}
4d.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}
5.-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}
6d.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}
7d.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
 )
2 (1/2,1/2,0) x,x+1/4,3/8 +1 {2xy|1/4,3/4,3/4}
8.-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}
9.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}
10.-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}
11d.-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+ (0,0,3/4) 1/4,1/2,z +1 {4z|3/4,1/4,3/4}
12.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- (0,0,1/4) 3/4,0,z +1 {4z-1|3/4,3/4,1/4}
13d.-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}
14.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}
15.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}
16d.-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
 )
2 x,-x+3/4,3/8 +1 {2-xy|3/4,3/4,3/4}
17.-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}'
18d.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}'
19.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}'
20d.-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}'
21d.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}'
22.-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}'
23.-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}'
24d.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}'
25d.-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}'
26.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}'
27d.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}'
28.-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}'
29.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}'
30d.-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}'
31d.-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}'
32.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}'
Show/Hide Derived operators due to the centring translations


Go to the Wyckoff Positions of 142.569 (I41/a'c'd')
Go to the extinction rules of 142.569 (I41/a'c'd')


Back to the list of magnetic space groups derived from I41/acd
Back to the list of Magnetic Space Groups

Bilbao Crystallographic Server
http://www.cryst.ehu.es 		For comments, please mail to
administrador.bcs@ehu.es