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Symmetry operations of the Double Space Group I41/a (No. 88)


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,-y,1/2+z
-is+,is-
(
  -1   0   0    1/2
   0  -1   0      0
   0   0   1    1/2
)
(
 -i  0
  0  i
)
{2001|1/2,0,1/2}
33/4-y,1/4+x,1/4+z
(1-i)√2s+/2,(1+i)√2s-/2
(
   0  -1   0    3/4
   1   0   0    1/4
   0   0   1    1/4
)
(
 (1-i)√2/2  0
  0 (1+i)√2/2
)
{4+001|3/4,1/4,1/4}
43/4+y,3/4-x,3/4+z
(1+i)√2s+/2,(1-i)√2s-/2
(
   0   1   0    3/4
  -1   0   0    3/4
   0   0   1    3/4
)
(
 (1+i)√2/2  0
  0 (1-i)√2/2
)
{4-001|3/4,3/4,3/4}
5-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}
61/2+x,y,1/2-z
-is+,is-
(
   1   0   0    1/2
   0   1   0      0
   0   0  -1    1/2
)
(
 -i  0
  0  i
)
{m001|1/2,0,1/2}
71/4+y,3/4-x,3/4-z
(1-i)√2s+/2,(1+i)√2s-/2
(
   0   1   0    1/4
  -1   0   0    3/4
   0   0  -1    3/4
)
(
 (1-i)√2/2  0
  0 (1+i)√2/2
)
{4+001|1/4,3/4,3/4}
81/4-y,1/4+x,1/4-z
(1+i)√2s+/2,(1-i)√2s-/2
(
   0  -1   0    1/4
   1   0   0    1/4
   0   0  -1    1/4
)
(
 (1+i)√2/2  0
  0 (1-i)√2/2
)
{4-001|1/4,1/4,1/4}
9x,y,z
-s+,-s-
(
   1   0   0      0
   0   1   0      0
   0   0   1      0
)
(
 -1  0
  0 -1
)
{d1|0,0,0}
101/2-x,-y,1/2+z
is+,-is-
(
  -1   0   0    1/2
   0  -1   0      0
   0   0   1    1/2
)
(
  i  0
  0 -i
)
{d2001|1/2,0,1/2}
113/4-y,1/4+x,1/4+z
-(1-i)√2s+/2,-(1+i)√2s-/2
(
   0  -1   0    3/4
   1   0   0    1/4
   0   0   1    1/4
)
(
 -(1-i)√2/2  0
  0 -(1+i)√2/2
)
{d4+001|3/4,1/4,1/4}
123/4+y,3/4-x,3/4+z
-(1+i)√2s+/2,-(1-i)√2s-/2
(
   0   1   0    3/4
  -1   0   0    3/4
   0   0   1    3/4
)
(
 -(1+i)√2/2  0
  0 -(1-i)√2/2
)
{d4-001|3/4,3/4,3/4}
13-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}
141/2+x,y,1/2-z
is+,-is-
(
   1   0   0    1/2
   0   1   0      0
   0   0  -1    1/2
)
(
  i  0
  0 -i
)
{dm001|1/2,0,1/2}
151/4+y,3/4-x,3/4-z
-(1-i)√2s+/2,-(1+i)√2s-/2
(
   0   1   0    1/4
  -1   0   0    3/4
   0   0  -1    3/4
)
(
 -(1-i)√2/2  0
  0 -(1+i)√2/2
)
{d4+001|1/4,3/4,3/4}
161/4-y,1/4+x,1/4-z
-(1+i)√2s+/2,-(1-i)√2s-/2
(
   0  -1   0    1/4
   1   0   0    1/4
   0   0  -1    1/4
)
(
 -(1+i)√2/2  0
  0 -(1-i)√2/2
)
{d4-001|1/4,1/4,1/4}
(1/2,1/2,1/2)+set


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