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Symmetry operations of the Double Space Group P3221 (No. 154)


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,2/3+z
(1+i3)s+/2,(1-i3)s-/2
(
   0  -1   0      0
   1  -1   0      0
   0   0   1    2/3
)
(
(1+i3)/2 0
0 (1-i3)/2
)
{3+001|0,0,2/3}
3-x+y,-x,1/3+z
(1-i3)s+/2,(1+i3)s-/2
(
  -1   1   0      0
  -1   0   0      0
   0   0   1    1/3
)
(
(1-i3)/2 0
0 (1+i3)/2
)
{3-001|0,0,1/3}
4y,x,-z
-(1+i3)s-/2,(1-i3)s+/2
(
   0   1   0      0
   1   0   0      0
   0   0  -1      0
)
(
0 -(1+i3)/2
(1-i3)/2 0
)
{2110|0,0,0}
5x-y,-y,1/3-z
-s-,s+
(
   1  -1   0      0
   0  -1   0      0
   0   0  -1    1/3
)
(
0 -1
1 0
)
{2100|0,0,1/3}
6-x,-x+y,2/3-z
-(1-i3)s-/2,(1+i3)s+/2
(
  -1   0   0      0
  -1   1   0      0
   0   0  -1    2/3
)
(
0 -(1-i3)/2
(1+i3)/2 0
)
{2010|0,0,2/3}
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,2/3+z
-(1+i3)s+/2,-(1-i3)s-/2
(
   0  -1   0      0
   1  -1   0      0
   0   0   1    2/3
)
(
-(1+i3)/2 0
0 -(1-i3)/2
)
{d3+001|0,0,2/3}
9-x+y,-x,1/3+z
-(1-i3)s+/2,-(1+i3)s-/2
(
  -1   1   0      0
  -1   0   0      0
   0   0   1    1/3
)
(
-(1-i3)/2 0
0 -(1+i3)/2
)
{d3-001|0,0,1/3}
10y,x,-z
(1+i3)s-/2,-(1-i3)s+/2
(
   0   1   0      0
   1   0   0      0
   0   0  -1      0
)
(
0 (1+i3)/2
-(1-i3)/2 0
)
{d2110|0,0,0}
11x-y,-y,1/3-z
s-,-s+
(
   1  -1   0      0
   0  -1   0      0
   0   0  -1    1/3
)
(
0 1
-1 0
)
{d2100|0,0,1/3}
12-x,-x+y,2/3-z
(1-i3)s-/2,-(1+i3)s+/2
(
  -1   0   0      0
  -1   1   0      0
   0   0  -1    2/3
)
(
0 (1-i3)/2
-(1+i3)/2 0
)
{d2010|0,0,2/3}


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