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General Positions of the 3D Crystallographic Point Group Th(m-3)


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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
13-x,-y,-z
(
 -1  0  0  
  0 -1  0  
  0  0 -1  
)
-1 0,0,0 -1
14x,y,-z
(
  1  0  0  
  0  1  0  
  0  0 -1  
)
m x,y,0 m001
15x,-y,z
(
  1  0  0  
  0 -1  0  
  0  0  1  
)
m x,0,z m010
16-x,y,z
(
 -1  0  0  
  0  1  0  
  0  0  1  
)
m 0,y,z m100
17-z,-x,-y
(
  0  0 -1  
 -1  0  0  
  0 -1  0  
)
-3+ x,x,x; 0,0,0 -3+111
18-z,x,y
(
  0  0 -1  
  1  0  0  
  0  1  0  
)
-3+ -x,x,-x; 0,0,0 -3+-11-1
19z,x,-y
(
  0  0  1  
  1  0  0  
  0 -1  0  
)
-3+ x,-x,-x; 0,0,0 -3+1-1-1
20z,-x,y
(
  0  0  1  
 -1  0  0  
  0  1  0  
)
-3+ -x,-x,x; 0,0,0 -3+-1-11
21-y,-z,-x
(
  0 -1  0  
  0  0 -1  
 -1  0  0  
)
-3- x,x,x; 0,0,0 -3-111
22y,-z,x
(
  0  1  0  
  0  0 -1  
  1  0  0  
)
-3- x,-x,-x; 0,0,0 -3-1-1-1
23-y,z,x
(
  0 -1  0  
  0  0  1  
  1  0  0  
)
-3- -x,-x,x; 0,0,0 -3--1-11
24y,z,-x
(
  0  1  0  
  0  0  1  
 -1  0  0  
)
-3- -x,x,-x; 0,0,0 -3--11-1



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