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General Positions of the 3D Crystallographic Point Group D3d(-31m) [Hexagonal 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
2-y,x-y,z
(
  0 -1  0  
  1 -1  0  
  0  0  1  
)
3+ 0,0,z 3+001
3-x+y,-x,z
(
 -1  1  0  
 -1  0  0  
  0  0  1  
)
3- 0,0,z 3-001
4-y,-x,-z
(
  0 -1  0  
 -1  0  0  
  0  0 -1  
)
2 x,-x,0 21-10
5-x+y,y,-z
(
 -1  1  0  
  0  1  0  
  0  0 -1  
)
2 x,2x,0 2120
6x,x-y,-z
(
  1  0  0  
  1 -1  0  
  0  0 -1  
)
2 2x,x,0 2210
7-x,-y,-z
(
 -1  0  0  
  0 -1  0  
  0  0 -1  
)
-1 0,0,0 -1
8y,-x+y,-z
(
  0  1  0  
 -1  1  0  
  0  0 -1  
)
-3+ 0,0,z; 0,0,0 -3+001
9x-y,x,-z
(
  1 -1  0  
  1  0  0  
  0  0 -1  
)
-3- 0,0,z; 0,0,0 -3-001
10y,x,z
(
  0  1  0  
  1  0  0  
  0  0  1  
)
m x,x,z m1-10
11x-y,-y,z
(
  1 -1  0  
  0 -1  0  
  0  0  1  
)
m 2x,-x,z m120
12-x,-x+y,z
(
 -1  0  0  
 -1  1  0  
  0  0  1  
)
m x,-2x,z m210

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


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