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General Positions of the 3D Crystallographic Point Group D3d(-3m) [Rhombohedral axes]


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No. (x,y,z) form Matrix form Symmetry operation
ITA Seitz
1x,y,z
(
  1  0  0  
  0  1  0  
  0  0  1  
)
1 1
2z,x,y
(
  0  0  1  
  1  0  0  
  0  1  0  
)
3+ x,x,x 3+111
3y,z,x
(
  0  1  0  
  0  0  1  
  1  0  0  
)
3- x,x,x 3-111
4-z,-y,-x
(
  0  0 -1  
  0 -1  0  
 -1  0  0  
)
2 -x,0,x 2-101
5-y,-x,-z
(
  0 -1  0  
 -1  0  0  
  0  0 -1  
)
2 x,-x,0 21-10
6-x,-z,-y
(
 -1  0  0  
  0  0 -1  
  0 -1  0  
)
2 0,y,-y 201-1
7-x,-y,-z
(
 -1  0  0  
  0 -1  0  
  0  0 -1  
)
-1 0,0,0 -1
8-z,-x,-y
(
  0  0 -1  
 -1  0  0  
  0 -1  0  
)
-3+ x,x,x; 0,0,0 -3+111
9-y,-z,-x
(
  0 -1  0  
  0  0 -1  
 -1  0  0  
)
-3- x,x,x; 0,0,0 -3-111
10z,y,x
(
  0  0  1  
  0  1  0  
  1  0  0  
)
m x,y,x m-101
11y,x,z
(
  0  1  0  
  1  0  0  
  0  0  1  
)
m x,x,z m1-10
12x,z,y
(
  1  0  0  
  0  0  1  
  0  1  0  
)
m x,y,y m01-1

[-31m hexagonal axes]
[-3m1 hexagonal axes]


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