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Symmetry operations of the Double Space Group I41 (No. 80)


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}
21/2-x,1/2-y,1/2+z
-is+,is-
(
  -1   0   0    1/2
   0  -1   0    1/2
   0   0   1    1/2
)
(
-i 0
0 i
)
{2001|1/2,1/2,1/2}
3-y,1/2+x,1/4+z
(1-i)2s+/2,(1+i)2s-/2
(
   0  -1   0      0
   1   0   0    1/2
   0   0   1    1/4
)
(
(1-i)2/2 0
0 (1+i)2/2
)
{4+001|0,1/2,1/4}
41/2+y,-x,3/4+z
(1+i)2s+/2,(1-i)2s-/2
(
   0   1   0    1/2
  -1   0   0      0
   0   0   1    3/4
)
(
(1+i)2/2 0
0 (1-i)2/2
)
{4-001|1/2,0,3/4}
5x,y,z
-s+,-s-
(
   1   0   0      0
   0   1   0      0
   0   0   1      0
)
(
-1 0
0 -1
)
{d1|0,0,0}
61/2-x,1/2-y,1/2+z
is+,-is-
(
  -1   0   0    1/2
   0  -1   0    1/2
   0   0   1    1/2
)
(
i 0
0 -i
)
{d2001|1/2,1/2,1/2}
7-y,1/2+x,1/4+z
-(1-i)2s+/2,-(1+i)2s-/2
(
   0  -1   0      0
   1   0   0    1/2
   0   0   1    1/4
)
(
-(1-i)2/2 0
0 -(1+i)2/2
)
{d4+001|0,1/2,1/4}
81/2+y,-x,3/4+z
-(1+i)2s+/2,-(1-i)2s-/2
(
   0   1   0    1/2
  -1   0   0      0
   0   0   1    3/4
)
(
-(1+i)2/2 0
0 -(1-i)2/2
)
{d4-001|1/2,0,3/4}
(1/2,1/2,1/2)+set


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