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General Positions of the 3D Crystallographic Point Group O(432)


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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-x,-y,z
(
 -1  0  0  
  0 -1  0  
  0  0  1
)
2 0,0,z 2001
3-x,y,-z
(
 -1  0  0  
  0  1  0  
  0  0 -1
)
2 0,y,0 2010
4x,-y,-z
(
  1  0  0  
  0 -1  0  
  0  0 -1
)
2 x,0,0 2100
5z,x,y
(
  0  0  1  
  1  0  0  
  0  1  0
)
3+ x,x,x 3+111
6z,-x,-y
(
  0  0  1  
 -1  0  0  
  0 -1  0
)
3+ -x,x,-x 3+-11-1
7-z,-x,y
(
  0  0 -1  
 -1  0  0  
  0  1  0
)
3+ x,-x,-x 3+1-1-1
8-z,x,-y
(
  0  0 -1  
  1  0  0  
  0 -1  0
)
3+ -x,-x,x 3+-1-11
9y,z,x
(
  0  1  0  
  0  0  1  
  1  0  0
)
3- x,x,x 3-111
10-y,z,-x
(
  0 -1  0  
  0  0  1  
 -1  0  0
)
3- x,-x,-x 3-1-1-1
11y,-z,-x
(
  0  1  0  
  0  0 -1  
 -1  0  0
)
3- -x,-x,x 3--1-11
12-y,-z,x
(
  0 -1  0  
  0  0 -1  
  1  0  0
)
3- -x,x,-x 3--11-1
13y,x,-z
(
  0  1  0  
  1  0  0  
  0  0 -1
)
2 x,x,0 2110
14-y,-x,-z
(
  0 -1  0  
 -1  0  0  
  0  0 -1
)
2 x,-x,0 21-10
15y,-x,z
(
  0  1  0  
 -1  0  0  
  0  0  1
)
4- 0,0,z 4-001
16-y,x,z
(
  0 -1  0  
  1  0  0  
  0  0  1
)
4+ 0,0,z 4+001
17x,z,-y
(
  1  0  0  
  0  0  1  
  0 -1  0
)
4- x,0,0 4-100
18-x,z,y
(
 -1  0  0  
  0  0  1  
  0  1  0
)
2 0,y,y 2011
19-x,-z,-y
(
 -1  0  0  
  0  0 -1  
  0 -1  0
)
2 0,y,-y 201-1
20x,-z,y
(
  1  0  0  
  0  0 -1  
  0  1  0
)
4+ x,0,0 4+100
21z,y,-x
(
  0  0  1  
  0  1  0  
 -1  0  0
)
4+ 0,y,0 4+010
22z,-y,x
(
  0  0  1  
  0 -1  0  
  1  0  0
)
2 x,0,x 2101
23-z,y,x
(
  0  0 -1  
  0  1  0  
  1  0  0
)
4- 0,y,0 4-010
24-z,-y,-x
(
  0  0 -1  
  0 -1  0  
 -1  0  0
)
2 -x,0,x 2-101



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