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

PI-43n [#218.84] (Type: 4 -- Type IV (klassengleiche))

[OG: IP-4'3m' #217.5.1584]

Operators of Group 218.84 (PI-43n)

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.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}
14.-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}
15.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}
16.-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}
17.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}
18.-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}
19.-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}
20.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}
21.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}
22.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}
23.-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}
24.-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}
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+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}'
27.-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}'
28.-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}'
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+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}'
31.-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}'
32.-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}'
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+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}'
35.-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}'
36.-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}'
37.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}'
38.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}'
39.-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}'
40.-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}'
41.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}'
42.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}'
43.-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}'
44.-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}'
45.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}'
46.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}'
47.-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}'
48.-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}'


Go to the Wyckoff Positions of 218.84 (PI-43n)
Go to the extinction rules of 218.84 (PI-43n)


Back to the list of magnetic space groups derived from I-43m
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