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Symmetry operations of the Double Space Group I23 (No. 197)


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-x,-y,z
-is+,is-
(
  -1   0   0      0
   0  -1   0      0
   0   0   1      0
)
(
 -i  0
  0  i
)
{2001|0,0,0}
3-x,y,-z
-s-,s+
(
  -1   0   0      0
   0   1   0      0
   0   0  -1      0
)
(
  0 -1
  1  0
)
{2010|0,0,0}
4x,-y,-z
-is-,-is+
(
   1   0   0      0
   0  -1   0      0
   0   0  -1      0
)
(
  0 -i
 -i  0
)
{2100|0,0,0}
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}
6z,-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}
7-z,-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}
8-z,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}
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,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}
11y,-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}
12-y,-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}
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}
14-x,-y,z
is+,-is-
(
  -1   0   0      0
   0  -1   0      0
   0   0   1      0
)
(
  i  0
  0 -i
)
{d2001|0,0,0}
15-x,y,-z
s-,-s+
(
  -1   0   0      0
   0   1   0      0
   0   0  -1      0
)
(
  0  1
 -1  0
)
{d2010|0,0,0}
16x,-y,-z
is-,is+
(
   1   0   0      0
   0  -1   0      0
   0   0  -1      0
)
(
 0 i
 i 0
)
{d2100|0,0,0}
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}
18z,-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}
19-z,-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}
20-z,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}
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,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}
23y,-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}
24-y,-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}
(1/2,1/2,1/2)+set


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