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Symmetry operations of the Double Space Group I213 (No. 199)


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}
13x,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
)
{d2001|1/2,0,1/2}
15-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}
161/2+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}
17z,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}
181/2+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}
191/2-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}
20-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}
21y,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}
22-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}
231/2+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}
241/2-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}
(1/2,1/2,1/2)+set


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