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Symmetry operations of the Double Space Group P61 (No. 169)


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,1/3+z
(1+i3)s+/2,(1-i3)s-/2
(
   0  -1   0      0
   1  -1   0      0
   0   0   1    1/3
)
(
(1+i3)/2 0
0 (1-i3)/2
)
{3+001|0,0,1/3}
3-x+y,-x,2/3+z
(1-i3)s+/2,(1+i3)s-/2
(
  -1   1   0      0
  -1   0   0      0
   0   0   1    2/3
)
(
(1-i3)/2 0
0 (1+i3)/2
)
{3-001|0,0,2/3}
4-x,-y,1/2+z
-is+,is-
(
  -1   0   0      0
   0  -1   0      0
   0   0   1    1/2
)
(
-i 0
0 i
)
{2001|0,0,1/2}
5y,-x+y,5/6+z
-(i-3)s+/2,(i+3)s-/2
(
   0   1   0      0
  -1   1   0      0
   0   0   1    5/6
)
(
-(i-3)/2 0
0 (i+3)/2
)
{6-001|0,0,5/6}
6x-y,x,1/6+z
(i+3)s+/2,-(i-3)s-/2
(
   1  -1   0      0
   1   0   0      0
   0   0   1    1/6
)
(
(i+3)/2 0
0 -(i-3)/2
)
{6+001|0,0,1/6}
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,1/3+z
-(1+i3)s+/2,-(1-i3)s-/2
(
   0  -1   0      0
   1  -1   0      0
   0   0   1    1/3
)
(
-(1+i3)/2 0
0 -(1-i3)/2
)
{d3+001|0,0,1/3}
9-x+y,-x,2/3+z
-(1-i3)s+/2,-(1+i3)s-/2
(
  -1   1   0      0
  -1   0   0      0
   0   0   1    2/3
)
(
-(1-i3)/2 0
0 -(1+i3)/2
)
{d3-001|0,0,2/3}
10-x,-y,1/2+z
is+,-is-
(
  -1   0   0      0
   0  -1   0      0
   0   0   1    1/2
)
(
i 0
0 -i
)
{d2001|0,0,1/2}
11y,-x+y,5/6+z
(i-3)s+/2,-(i+3)s-/2
(
   0   1   0      0
  -1   1   0      0
   0   0   1    5/6
)
(
(i-3)/2 0
0 -(i+3)/2
)
{d6-001|0,0,5/6}
12x-y,x,1/6+z
-(i+3)s+/2,(i-3)s-/2
(
   1  -1   0      0
   1   0   0      0
   0   0   1    1/6
)
(
-(i+3)/2 0
0 (i-3)/2
)
{d6+001|0,0,1/6}


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