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Symmetry operations of the Double Space Group R-3 (No. 148)


N Shorthand
notation
Matrix presentation Seitz symbol
(0,0,0)+set
1x,y,z
s+,s-
(
   1   0   0      0
   0   1   0      0
   0   0   1      0
)
(
1 0
0 1
)
{1|0,0,0}
2-y,x-y,z
(1+i3)s+/2,(1-i3)s-/2
(
   0  -1   0      0
   1  -1   0      0
   0   0   1      0
)
(
(1+i3)/2 0
0 (1-i3)/2
)
{3+001|0,0,0}
3-x+y,-x,z
(1-i3)s+/2,(1+i3)s-/2
(
  -1   1   0      0
  -1   0   0      0
   0   0   1      0
)
(
(1-i3)/2 0
0 (1+i3)/2
)
{3-001|0,0,0}
4-x,-y,-z
s+,s-
(
  -1   0   0      0
   0  -1   0      0
   0   0  -1      0
)
(
1 0
0 1
)
{1|0,0,0}
5y,-x+y,-z
(1+i3)s+/2,(1-i3)s-/2
(
   0   1   0      0
  -1   1   0      0
   0   0  -1      0
)
(
(1+i3)/2 0
0 (1-i3)/2
)
{3+001|0,0,0}
6x-y,x,-z
(1-i3)s+/2,(1+i3)s-/2
(
   1  -1   0      0
   1   0   0      0
   0   0  -1      0
)
(
(1-i3)/2 0
0 (1+i3)/2
)
{3-001|0,0,0}
7x,y,z
-s+,-s-
(
   1   0   0      0
   0   1   0      0
   0   0   1      0
)
(
-1 0
0 -1
)
{d1|0,0,0}
8-y,x-y,z
-(1+i3)s+/2,-(1-i3)s-/2
(
   0  -1   0      0
   1  -1   0      0
   0   0   1      0
)
(
-(1+i3)/2 0
0 -(1-i3)/2
)
{d3+001|0,0,0}
9-x+y,-x,z
-(1-i3)s+/2,-(1+i3)s-/2
(
  -1   1   0      0
  -1   0   0      0
   0   0   1      0
)
(
-(1-i3)/2 0
0 -(1+i3)/2
)
{d3-001|0,0,0}
10-x,-y,-z
-s+,-s-
(
  -1   0   0      0
   0  -1   0      0
   0   0  -1      0
)
(
-1 0
0 -1
)
{d1|0,0,0}
11y,-x+y,-z
-(1+i3)s+/2,-(1-i3)s-/2
(
   0   1   0      0
  -1   1   0      0
   0   0  -1      0
)
(
-(1+i3)/2 0
0 -(1-i3)/2
)
{d3+001|0,0,0}
12x-y,x,-z
-(1-i3)s+/2,-(1+i3)s-/2
(
   1  -1   0      0
   1   0   0      0
   0   0  -1      0
)
(
-(1-i3)/2 0
0 -(1+i3)/2
)
{d3-001|0,0,0}
(2/3,1/3,1/3)+set
(1/3,2/3,2/3)+set


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