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Symmetry operations of the Double Space Group Fd-3 (No. 203)


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}
23/4-x,3/4-y,z
-is+,is-
(
  -1   0   0    3/4
   0  -1   0    3/4
   0   0   1      0
)
(
-i 0
0 i
)
{2001|3/4,3/4,0}
33/4-x,y,3/4-z
-s-,s+
(
  -1   0   0    3/4
   0   1   0      0
   0   0  -1    3/4
)
(
0 -1
1 0
)
{2010|3/4,0,3/4}
4x,3/4-y,3/4-z
-is-,-is+
(
   1   0   0      0
   0  -1   0    3/4
   0   0  -1    3/4
)
(
0 -i
-i 0
)
{2100|0,3/4,3/4}
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,3/4-x,3/4-y
(1+i)s+/2-(1-i)s-/2,(1+i)s+/2+(1-i)s-/2
(
   0   0   1      0
  -1   0   0    3/4
   0  -1   0    3/4
)
(
(1+i)/2 -(1-i)/2
(1+i)/2 (1-i)/2
)
{3+111|0,3/4,3/4}
73/4-z,3/4-x,y
(1+i)s+/2+(1-i)s-/2,-(1+i)s+/2+(1-i)s-/2
(
   0   0  -1    3/4
  -1   0   0    3/4
   0   1   0      0
)
(
(1+i)/2 (1-i)/2
-(1+i)/2 (1-i)/2
)
{3+111|3/4,3/4,0}
83/4-z,x,3/4-y
(1-i)s+/2+(1+i)s-/2,-(1-i)s+/2+(1+i)s-/2
(
   0   0  -1    3/4
   1   0   0      0
   0  -1   0    3/4
)
(
(1-i)/2 (1+i)/2
-(1-i)/2 (1+i)/2
)
{3+111|3/4,0,3/4}
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}
103/4-y,z,3/4-x
(1-i)s+/2-(1-i)s-/2,(1+i)s+/2+(1+i)s-/2
(
   0  -1   0    3/4
   0   0   1      0
  -1   0   0    3/4
)
(
(1-i)/2 -(1-i)/2
(1+i)/2 (1+i)/2
)
{3-111|3/4,0,3/4}
11y,3/4-z,3/4-x
(1+i)s+/2-(1+i)s-/2,(1-i)s+/2+(1-i)s-/2
(
   0   1   0      0
   0   0  -1    3/4
  -1   0   0    3/4
)
(
(1+i)/2 -(1+i)/2
(1-i)/2 (1-i)/2
)
{3-111|0,3/4,3/4}
123/4-y,3/4-z,x
(1-i)s+/2+(1-i)s-/2,-(1+i)s+/2+(1+i)s-/2
(
   0  -1   0    3/4
   0   0  -1    3/4
   1   0   0      0
)
(
(1-i)/2 (1-i)/2
-(1+i)/2 (1+i)/2
)
{3-111|3/4,3/4,0}
13-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}
141/4+x,1/4+y,-z
-is+,is-
(
   1   0   0    1/4
   0   1   0    1/4
   0   0  -1      0
)
(
-i 0
0 i
)
{m001|1/4,1/4,0}
151/4+x,-y,1/4+z
-s-,s+
(
   1   0   0    1/4
   0  -1   0      0
   0   0   1    1/4
)
(
0 -1
1 0
)
{m010|1/4,0,1/4}
16-x,1/4+y,1/4+z
-is-,-is+
(
  -1   0   0      0
   0   1   0    1/4
   0   0   1    1/4
)
(
0 -i
-i 0
)
{m100|0,1/4,1/4}
17-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}
18-z,1/4+x,1/4+y
(1+i)s+/2-(1-i)s-/2,(1+i)s+/2+(1-i)s-/2
(
   0   0  -1      0
   1   0   0    1/4
   0   1   0    1/4
)
(
(1+i)/2 -(1-i)/2
(1+i)/2 (1-i)/2
)
{3+111|0,1/4,1/4}
191/4+z,1/4+x,-y
(1+i)s+/2+(1-i)s-/2,-(1+i)s+/2+(1-i)s-/2
(
   0   0   1    1/4
   1   0   0    1/4
   0  -1   0      0
)
(
(1+i)/2 (1-i)/2
-(1+i)/2 (1-i)/2
)
{3+111|1/4,1/4,0}
201/4+z,-x,1/4+y
(1-i)s+/2+(1+i)s-/2,-(1-i)s+/2+(1+i)s-/2
(
   0   0   1    1/4
  -1   0   0      0
   0   1   0    1/4
)
(
(1-i)/2 (1+i)/2
-(1-i)/2 (1+i)/2
)
{3+111|1/4,0,1/4}
21-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}
221/4+y,-z,1/4+x
(1-i)s+/2-(1-i)s-/2,(1+i)s+/2+(1+i)s-/2
(
   0   1   0    1/4
   0   0  -1      0
   1   0   0    1/4
)
(
(1-i)/2 -(1-i)/2
(1+i)/2 (1+i)/2
)
{3-111|1/4,0,1/4}
23-y,1/4+z,1/4+x
(1+i)s+/2-(1+i)s-/2,(1-i)s+/2+(1-i)s-/2
(
   0  -1   0      0
   0   0   1    1/4
   1   0   0    1/4
)
(
(1+i)/2 -(1+i)/2
(1-i)/2 (1-i)/2
)
{3-111|0,1/4,1/4}
241/4+y,1/4+z,-x
(1-i)s+/2+(1-i)s-/2,-(1+i)s+/2+(1+i)s-/2
(
   0   1   0    1/4
   0   0   1    1/4
  -1   0   0      0
)
(
(1-i)/2 (1-i)/2
-(1+i)/2 (1+i)/2
)
{3-111|1/4,1/4,0}
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}
263/4-x,3/4-y,z
is+,-is-
(
  -1   0   0    3/4
   0  -1   0    3/4
   0   0   1      0
)
(
i 0
0 -i
)
{d2001|3/4,3/4,0}
273/4-x,y,3/4-z
s-,-s+
(
  -1   0   0    3/4
   0   1   0      0
   0   0  -1    3/4
)
(
0 1
-1 0
)
{d2010|3/4,0,3/4}
28x,3/4-y,3/4-z
is-,is+
(
   1   0   0      0
   0  -1   0    3/4
   0   0  -1    3/4
)
(
0 i
i 0
)
{d2100|0,3/4,3/4}
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}
30z,3/4-x,3/4-y
-(1+i)s+/2+(1-i)s-/2,-(1+i)s+/2-(1-i)s-/2
(
   0   0   1      0
  -1   0   0    3/4
   0  -1   0    3/4
)
(
-(1+i)/2 (1-i)/2
-(1+i)/2 -(1-i)/2
)
{d3+111|0,3/4,3/4}
313/4-z,3/4-x,y
-(1+i)s+/2-(1-i)s-/2,(1+i)s+/2-(1-i)s-/2
(
   0   0  -1    3/4
  -1   0   0    3/4
   0   1   0      0
)
(
-(1+i)/2 -(1-i)/2
(1+i)/2 -(1-i)/2
)
{d3+111|3/4,3/4,0}
323/4-z,x,3/4-y
-(1-i)s+/2-(1+i)s-/2,(1-i)s+/2-(1+i)s-/2
(
   0   0  -1    3/4
   1   0   0      0
   0  -1   0    3/4
)
(
-(1-i)/2 -(1+i)/2
(1-i)/2 -(1+i)/2
)
{d3+111|3/4,0,3/4}
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}
343/4-y,z,3/4-x
-(1-i)s+/2+(1-i)s-/2,-(1+i)s+/2-(1+i)s-/2
(
   0  -1   0    3/4
   0   0   1      0
  -1   0   0    3/4
)
(
-(1-i)/2 (1-i)/2
-(1+i)/2 -(1+i)/2
)
{d3-111|3/4,0,3/4}
35y,3/4-z,3/4-x
-(1+i)s+/2+(1+i)s-/2,-(1-i)s+/2-(1-i)s-/2
(
   0   1   0      0
   0   0  -1    3/4
  -1   0   0    3/4
)
(
-(1+i)/2 (1+i)/2
-(1-i)/2 -(1-i)/2
)
{d3-111|0,3/4,3/4}
363/4-y,3/4-z,x
-(1-i)s+/2-(1-i)s-/2,(1+i)s+/2-(1+i)s-/2
(
   0  -1   0    3/4
   0   0  -1    3/4
   1   0   0      0
)
(
-(1-i)/2 -(1-i)/2
(1+i)/2 -(1+i)/2
)
{d3-111|3/4,3/4,0}
37-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}
381/4+x,1/4+y,-z
is+,-is-
(
   1   0   0    1/4
   0   1   0    1/4
   0   0  -1      0
)
(
i 0
0 -i
)
{dm001|1/4,1/4,0}
391/4+x,-y,1/4+z
s-,-s+
(
   1   0   0    1/4
   0  -1   0      0
   0   0   1    1/4
)
(
0 1
-1 0
)
{dm010|1/4,0,1/4}
40-x,1/4+y,1/4+z
is-,is+
(
  -1   0   0      0
   0   1   0    1/4
   0   0   1    1/4
)
(
0 i
i 0
)
{dm100|0,1/4,1/4}
41-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}
42-z,1/4+x,1/4+y
-(1+i)s+/2+(1-i)s-/2,-(1+i)s+/2-(1-i)s-/2
(
   0   0  -1      0
   1   0   0    1/4
   0   1   0    1/4
)
(
-(1+i)/2 (1-i)/2
-(1+i)/2 -(1-i)/2
)
{d3+111|0,1/4,1/4}
431/4+z,1/4+x,-y
-(1+i)s+/2-(1-i)s-/2,(1+i)s+/2-(1-i)s-/2
(
   0   0   1    1/4
   1   0   0    1/4
   0  -1   0      0
)
(
-(1+i)/2 -(1-i)/2
(1+i)/2 -(1-i)/2
)
{d3+111|1/4,1/4,0}
441/4+z,-x,1/4+y
-(1-i)s+/2-(1+i)s-/2,(1-i)s+/2-(1+i)s-/2
(
   0   0   1    1/4
  -1   0   0      0
   0   1   0    1/4
)
(
-(1-i)/2 -(1+i)/2
(1-i)/2 -(1+i)/2
)
{d3+111|1/4,0,1/4}
45-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}
461/4+y,-z,1/4+x
-(1-i)s+/2+(1-i)s-/2,-(1+i)s+/2-(1+i)s-/2
(
   0   1   0    1/4
   0   0  -1      0
   1   0   0    1/4
)
(
-(1-i)/2 (1-i)/2
-(1+i)/2 -(1+i)/2
)
{d3-111|1/4,0,1/4}
47-y,1/4+z,1/4+x
-(1+i)s+/2+(1+i)s-/2,-(1-i)s+/2-(1-i)s-/2
(
   0  -1   0      0
   0   0   1    1/4
   1   0   0    1/4
)
(
-(1+i)/2 (1+i)/2
-(1-i)/2 -(1-i)/2
)
{d3-111|0,1/4,1/4}
481/4+y,1/4+z,-x
-(1-i)s+/2-(1-i)s-/2,(1+i)s+/2-(1+i)s-/2
(
   0   1   0    1/4
   0   0   1    1/4
  -1   0   0      0
)
(
-(1-i)/2 -(1-i)/2
(1+i)/2 -(1+i)/2
)
{d3-111|1/4,1/4,0}
(0,1/2,1/2)+set
(1/2,0,1/2)+set
(1/2,1/2,0)+set


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