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Symmetry operations of the Double Space Group I-43d (No. 220)


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}
3-x,1/2+y,1/2-z
-s-,s+
(
  -1   0   0      0
   0   1   0    1/2
   0   0  -1    1/2
)
(
  0 -1
  1  0
)
{2010|0,1/2,1/2}
41/2+x,1/2-y,-z
-is-,-is+
(
   1   0   0    1/2
   0  -1   0    1/2
   0   0  -1      0
)
(
  0 -i
 -i  0
)
{2100|1/2,1/2,0}
5z,x,y
(1-i)s+/2-(1+i)s-/2,(1-i)s+/2+(1+i)s-/2
(
   0   0   1      0
   1   0   0      0
   0   1   0      0
)
(
  (1-i)/2 -(1+i)/2
  (1-i)/2  (1+i)/2
)
{3+111|0,0,0}
61/2+z,1/2-x,-y
(1+i)s+/2-(1-i)s-/2,(1+i)s+/2+(1-i)s-/2
(
   0   0   1    1/2
  -1   0   0    1/2
   0  -1   0      0
)
(
  (1+i)/2 -(1-i)/2
  (1+i)/2  (1-i)/2
)
{3+111|1/2,1/2,0}
71/2-z,-x,1/2+y
(1+i)s+/2+(1-i)s-/2,-(1+i)s+/2+(1-i)s-/2
(
   0   0  -1    1/2
  -1   0   0      0
   0   1   0    1/2
)
(
  (1+i)/2  (1-i)/2
 -(1+i)/2  (1-i)/2
)
{3+111|1/2,0,1/2}
8-z,1/2+x,1/2-y
(1-i)s+/2+(1+i)s-/2,-(1-i)s+/2+(1+i)s-/2
(
   0   0  -1      0
   1   0   0    1/2
   0  -1   0    1/2
)
(
  (1-i)/2  (1+i)/2
 -(1-i)/2  (1+i)/2
)
{3+111|0,1/2,1/2}
9y,z,x
(1+i)s+/2+(1+i)s-/2,-(1-i)s+/2+(1-i)s-/2
(
   0   1   0      0
   0   0   1      0
   1   0   0      0
)
(
  (1+i)/2  (1+i)/2
 -(1-i)/2  (1-i)/2
)
{3-111|0,0,0}
10-y,1/2+z,1/2-x
(1-i)s+/2-(1-i)s-/2,(1+i)s+/2+(1+i)s-/2
(
   0  -1   0      0
   0   0   1    1/2
  -1   0   0    1/2
)
(
  (1-i)/2 -(1-i)/2
  (1+i)/2  (1+i)/2
)
{3-111|0,1/2,1/2}
111/2+y,1/2-z,-x
(1+i)s+/2-(1+i)s-/2,(1-i)s+/2+(1-i)s-/2
(
   0   1   0    1/2
   0   0  -1    1/2
  -1   0   0      0
)
(
  (1+i)/2 -(1+i)/2
  (1-i)/2  (1-i)/2
)
{3-111|1/2,1/2,0}
121/2-y,-z,1/2+x
(1-i)s+/2+(1-i)s-/2,-(1+i)s+/2+(1+i)s-/2
(
   0  -1   0    1/2
   0   0  -1      0
   1   0   0    1/2
)
(
  (1-i)/2  (1-i)/2
 -(1+i)/2  (1+i)/2
)
{3-111|1/2,0,1/2}
131/4+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
)
(
  0 -(1-i)√2/2
  (1+i)√2/2  0
)
{m110|1/4,1/4,1/4}
141/4-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
)
(
  0 -(1+i)√2/2
  (1-i)√2/2  0
)
{m110|1/4,3/4,3/4}
153/4+y,1/4-x,3/4-z
(1-i)√2s+/2,(1+i)√2s-/2
(
   0   1   0    3/4
  -1   0   0    1/4
   0   0  -1    3/4
)
(
 (1-i)√2/2  0
  0 (1+i)√2/2
)
{4+001|3/4,1/4,3/4}
163/4-y,3/4+x,1/4-z
(1+i)√2s+/2,(1-i)√2s-/2
(
   0  -1   0    3/4
   1   0   0    3/4
   0   0  -1    1/4
)
(
 (1+i)√2/2  0
  0 (1-i)√2/2
)
{4-001|3/4,3/4,1/4}
171/4+x,1/4+z,1/4+y
-i√2s+/2+√2s-/2,-√2s+/2+i√2s-/2
(
   1   0   0    1/4
   0   0   1    1/4
   0   1   0    1/4
)
(
 -i√2/2  √2/2
  -√2/2  i√2/2
)
{m011|1/4,1/4,1/4}
183/4-x,3/4+z,1/4-y
√2s+/2-i√2s-/2,-i√2s+/2+√2s-/2
(
  -1   0   0    3/4
   0   0   1    3/4
   0  -1   0    1/4
)
(
  √2/2 -i√2/2
 -i√2/2  √2/2
)
{4+100|3/4,3/4,1/4}
191/4-x,3/4-z,3/4+y
√2s+/2+i√2s-/2,i√2s+/2+√2s-/2
(
  -1   0   0    1/4
   0   0  -1    3/4
   0   1   0    3/4
)
(
  √2/2 i√2/2
 i√2/2  √2/2
)
{4-100|1/4,3/4,3/4}
203/4+x,1/4-z,3/4-y
i√2s+/2+√2s-/2,-√2s+/2-i√2s-/2
(
   1   0   0    3/4
   0   0  -1    1/4
   0  -1   0    3/4
)
(
  i√2/2  √2/2
  -√2/2 -i√2/2
)
{m011|3/4,1/4,3/4}
211/4+z,1/4+y,1/4+x
i√2s+/2-i√2s-/2,-i√2s+/2-i√2s-/2
(
   0   0   1    1/4
   0   1   0    1/4
   1   0   0    1/4
)
(
  i√2/2 -i√2/2
 -i√2/2 -i√2/2
)
{m101|1/4,1/4,1/4}
223/4+z,1/4-y,3/4-x
√2s+/2+√2s-/2,-√2s+/2+√2s-/2
(
   0   0   1    3/4
   0  -1   0    1/4
  -1   0   0    3/4
)
(
  √2/2  √2/2
 -√2/2  √2/2
)
{4-010|3/4,1/4,3/4}
233/4-z,3/4+y,1/4-x
-i√2s+/2-i√2s-/2,-i√2s+/2+i√2s-/2
(
   0   0  -1    3/4
   0   1   0    3/4
  -1   0   0    1/4
)
(
 -i√2/2 -i√2/2
 -i√2/2  i√2/2
)
{m101|3/4,3/4,1/4}
241/4-z,3/4-y,3/4+x
√2s+/2-√2s-/2,√2s+/2+√2s-/2
(
   0   0  -1    1/4
   0  -1   0    3/4
   1   0   0    3/4
)
(
  √2/2 -√2/2
  √2/2  √2/2
)
{4+010|1/4,3/4,3/4}
25x,y,z
-s+,-s-
(
   1   0   0      0
   0   1   0      0
   0   0   1      0
)
(
 -1  0
  0 -1
)
{d1|0,0,0}
261/2-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}
27-x,1/2+y,1/2-z
s-,-s+
(
  -1   0   0      0
   0   1   0    1/2
   0   0  -1    1/2
)
(
  0  1
 -1  0
)
{d2010|0,1/2,1/2}
281/2+x,1/2-y,-z
is-,is+
(
   1   0   0    1/2
   0  -1   0    1/2
   0   0  -1      0
)
(
 0 i
 i 0
)
{d2100|1/2,1/2,0}
29z,x,y
-(1-i)s+/2+(1+i)s-/2,-(1-i)s+/2-(1+i)s-/2
(
   0   0   1      0
   1   0   0      0
   0   1   0      0
)
(
 -(1-i)/2  (1+i)/2
 -(1-i)/2 -(1+i)/2
)
{d3+111|0,0,0}
301/2+z,1/2-x,-y
-(1+i)s+/2+(1-i)s-/2,-(1+i)s+/2-(1-i)s-/2
(
   0   0   1    1/2
  -1   0   0    1/2
   0  -1   0      0
)
(
 -(1+i)/2  (1-i)/2
 -(1+i)/2 -(1-i)/2
)
{d3+111|1/2,1/2,0}
311/2-z,-x,1/2+y
-(1+i)s+/2-(1-i)s-/2,(1+i)s+/2-(1-i)s-/2
(
   0   0  -1    1/2
  -1   0   0      0
   0   1   0    1/2
)
(
 -(1+i)/2 -(1-i)/2
  (1+i)/2 -(1-i)/2
)
{d3+111|1/2,0,1/2}
32-z,1/2+x,1/2-y
-(1-i)s+/2-(1+i)s-/2,(1-i)s+/2-(1+i)s-/2
(
   0   0  -1      0
   1   0   0    1/2
   0  -1   0    1/2
)
(
 -(1-i)/2 -(1+i)/2
  (1-i)/2 -(1+i)/2
)
{d3+111|0,1/2,1/2}
33y,z,x
-(1+i)s+/2-(1+i)s-/2,(1-i)s+/2-(1-i)s-/2
(
   0   1   0      0
   0   0   1      0
   1   0   0      0
)
(
 -(1+i)/2 -(1+i)/2
  (1-i)/2 -(1-i)/2
)
{d3-111|0,0,0}
34-y,1/2+z,1/2-x
-(1-i)s+/2+(1-i)s-/2,-(1+i)s+/2-(1+i)s-/2
(
   0  -1   0      0
   0   0   1    1/2
  -1   0   0    1/2
)
(
 -(1-i)/2  (1-i)/2
 -(1+i)/2 -(1+i)/2
)
{d3-111|0,1/2,1/2}
351/2+y,1/2-z,-x
-(1+i)s+/2+(1+i)s-/2,-(1-i)s+/2-(1-i)s-/2
(
   0   1   0    1/2
   0   0  -1    1/2
  -1   0   0      0
)
(
 -(1+i)/2  (1+i)/2
 -(1-i)/2 -(1-i)/2
)
{d3-111|1/2,1/2,0}
361/2-y,-z,1/2+x
-(1-i)s+/2-(1-i)s-/2,(1+i)s+/2-(1+i)s-/2
(
   0  -1   0    1/2
   0   0  -1      0
   1   0   0    1/2
)
(
 -(1-i)/2 -(1-i)/2
  (1+i)/2 -(1+i)/2
)
{d3-111|1/2,0,1/2}
371/4+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
)
(
  0  (1-i)√2/2
 -(1+i)√2/2  0
)
{dm110|1/4,1/4,1/4}
381/4-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
)
(
  0  (1+i)√2/2
 -(1-i)√2/2  0
)
{dm110|1/4,3/4,3/4}
393/4+y,1/4-x,3/4-z
-(1-i)√2s+/2,-(1+i)√2s-/2
(
   0   1   0    3/4
  -1   0   0    1/4
   0   0  -1    3/4
)
(
 -(1-i)√2/2  0
  0 -(1+i)√2/2
)
{d4+001|3/4,1/4,3/4}
403/4-y,3/4+x,1/4-z
-(1+i)√2s+/2,-(1-i)√2s-/2
(
   0  -1   0    3/4
   1   0   0    3/4
   0   0  -1    1/4
)
(
 -(1+i)√2/2  0
  0 -(1-i)√2/2
)
{d4-001|3/4,3/4,1/4}
411/4+x,1/4+z,1/4+y
i√2s+/2-√2s-/2,√2s+/2-i√2s-/2
(
   1   0   0    1/4
   0   0   1    1/4
   0   1   0    1/4
)
(
  i√2/2  -√2/2
  √2/2 -i√2/2
)
{dm011|1/4,1/4,1/4}
423/4-x,3/4+z,1/4-y
-√2s+/2+i√2s-/2,i√2s+/2-√2s-/2
(
  -1   0   0    3/4
   0   0   1    3/4
   0  -1   0    1/4
)
(
 -√2/2 i√2/2
 i√2/2 -√2/2
)
{d4+100|3/4,3/4,1/4}
431/4-x,3/4-z,3/4+y
-√2s+/2-i√2s-/2,-i√2s+/2-√2s-/2
(
  -1   0   0    1/4
   0   0  -1    3/4
   0   1   0    3/4
)
(
  -√2/2 -i√2/2
 -i√2/2  -√2/2
)
{d4-100|1/4,3/4,3/4}
443/4+x,1/4-z,3/4-y
-i√2s+/2-√2s-/2,√2s+/2+i√2s-/2
(
   1   0   0    3/4
   0   0  -1    1/4
   0  -1   0    3/4
)
(
 -i√2/2  -√2/2
  √2/2  i√2/2
)
{dm011|3/4,1/4,3/4}
451/4+z,1/4+y,1/4+x
-i√2s+/2+i√2s-/2,i√2s+/2+i√2s-/2
(
   0   0   1    1/4
   0   1   0    1/4
   1   0   0    1/4
)
(
 -i√2/2  i√2/2
  i√2/2  i√2/2
)
{dm101|1/4,1/4,1/4}
463/4+z,1/4-y,3/4-x
-√2s+/2-√2s-/2,√2s+/2-√2s-/2
(
   0   0   1    3/4
   0  -1   0    1/4
  -1   0   0    3/4
)
(
 -√2/2 -√2/2
  √2/2 -√2/2
)
{d4-010|3/4,1/4,3/4}
473/4-z,3/4+y,1/4-x
i√2s+/2+i√2s-/2,i√2s+/2-i√2s-/2
(
   0   0  -1    3/4
   0   1   0    3/4
  -1   0   0    1/4
)
(
  i√2/2  i√2/2
  i√2/2 -i√2/2
)
{dm101|3/4,3/4,1/4}
481/4-z,3/4-y,3/4+x
-√2s+/2+√2s-/2,-√2s+/2-√2s-/2
(
   0   0  -1    1/4
   0  -1   0    3/4
   1   0   0    3/4
)
(
 -√2/2  √2/2
 -√2/2 -√2/2
)
{d4+010|1/4,3/4,3/4}
(1/2,1/2,1/2)+set


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