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Symmetry operations of the Double Space Group I432 (No. 211)


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}
13y,x,-z
-(1+i)√2s-/2,(1-i)√2s+/2
(
   0   1   0      0
   1   0   0      0
   0   0  -1      0
)
(
  0 -(1+i)√2/2
  (1-i)√2/2  0
)
{2110|0,0,0}
14-y,-x,-z
-(1-i)√2s-/2,(1+i)√2s+/2
(
   0  -1   0      0
  -1   0   0      0
   0   0  -1      0
)
(
  0 -(1-i)√2/2
  (1+i)√2/2  0
)
{2110|0,0,0}
15y,-x,z
(1+i)√2s+/2,(1-i)√2s-/2
(
   0   1   0      0
  -1   0   0      0
   0   0   1      0
)
(
 (1+i)√2/2  0
  0 (1-i)√2/2
)
{4-001|0,0,0}
16-y,x,z
(1-i)√2s+/2,(1+i)√2s-/2
(
   0  -1   0      0
   1   0   0      0
   0   0   1      0
)
(
 (1-i)√2/2  0
  0 (1+i)√2/2
)
{4+001|0,0,0}
17x,z,-y
√2s+/2+i√2s-/2,i√2s+/2+√2s-/2
(
   1   0   0      0
   0   0   1      0
   0  -1   0      0
)
(
  √2/2 i√2/2
 i√2/2  √2/2
)
{4-100|0,0,0}
18-x,z,y
i√2s+/2+√2s-/2,-√2s+/2-i√2s-/2
(
  -1   0   0      0
   0   0   1      0
   0   1   0      0
)
(
  i√2/2  √2/2
  -√2/2 -i√2/2
)
{2011|0,0,0}
19-x,-z,-y
-i√2s+/2+√2s-/2,-√2s+/2+i√2s-/2
(
  -1   0   0      0
   0   0  -1      0
   0  -1   0      0
)
(
 -i√2/2  √2/2
  -√2/2  i√2/2
)
{2011|0,0,0}
20x,-z,y
√2s+/2-i√2s-/2,-i√2s+/2+√2s-/2
(
   1   0   0      0
   0   0  -1      0
   0   1   0      0
)
(
  √2/2 -i√2/2
 -i√2/2  √2/2
)
{4+100|0,0,0}
21z,y,-x
√2s+/2-√2s-/2,√2s+/2+√2s-/2
(
   0   0   1      0
   0   1   0      0
  -1   0   0      0
)
(
  √2/2 -√2/2
  √2/2  √2/2
)
{4+010|0,0,0}
22z,-y,x
-i√2s+/2-i√2s-/2,-i√2s+/2+i√2s-/2
(
   0   0   1      0
   0  -1   0      0
   1   0   0      0
)
(
 -i√2/2 -i√2/2
 -i√2/2  i√2/2
)
{2101|0,0,0}
23-z,y,x
√2s+/2+√2s-/2,-√2s+/2+√2s-/2
(
   0   0  -1      0
   0   1   0      0
   1   0   0      0
)
(
  √2/2  √2/2
 -√2/2  √2/2
)
{4-010|0,0,0}
24-z,-y,-x
i√2s+/2-i√2s-/2,-i√2s+/2-i√2s-/2
(
   0   0  -1      0
   0  -1   0      0
  -1   0   0      0
)
(
  i√2/2 -i√2/2
 -i√2/2 -i√2/2
)
{2101|0,0,0}
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}
26-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}
27-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}
28x,-y,-z
is-,is+
(
   1   0   0      0
   0  -1   0      0
   0   0  -1      0
)
(
 0 i
 i 0
)
{d2100|0,0,0}
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}
30z,-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}
31-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}
32-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}
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,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}
35y,-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}
36-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}
37y,x,-z
(1+i)√2s-/2,-(1-i)√2s+/2
(
   0   1   0      0
   1   0   0      0
   0   0  -1      0
)
(
  0  (1+i)√2/2
 -(1-i)√2/2  0
)
{d2110|0,0,0}
38-y,-x,-z
(1-i)√2s-/2,-(1+i)√2s+/2
(
   0  -1   0      0
  -1   0   0      0
   0   0  -1      0
)
(
  0  (1-i)√2/2
 -(1+i)√2/2  0
)
{d2110|0,0,0}
39y,-x,z
-(1+i)√2s+/2,-(1-i)√2s-/2
(
   0   1   0      0
  -1   0   0      0
   0   0   1      0
)
(
 -(1+i)√2/2  0
  0 -(1-i)√2/2
)
{d4-001|0,0,0}
40-y,x,z
-(1-i)√2s+/2,-(1+i)√2s-/2
(
   0  -1   0      0
   1   0   0      0
   0   0   1      0
)
(
 -(1-i)√2/2  0
  0 -(1+i)√2/2
)
{d4+001|0,0,0}
41x,z,-y
-√2s+/2-i√2s-/2,-i√2s+/2-√2s-/2
(
   1   0   0      0
   0   0   1      0
   0  -1   0      0
)
(
  -√2/2 -i√2/2
 -i√2/2  -√2/2
)
{d4-100|0,0,0}
42-x,z,y
-i√2s+/2-√2s-/2,√2s+/2+i√2s-/2
(
  -1   0   0      0
   0   0   1      0
   0   1   0      0
)
(
 -i√2/2  -√2/2
  √2/2  i√2/2
)
{d2011|0,0,0}
43-x,-z,-y
i√2s+/2-√2s-/2,√2s+/2-i√2s-/2
(
  -1   0   0      0
   0   0  -1      0
   0  -1   0      0
)
(
  i√2/2  -√2/2
  √2/2 -i√2/2
)
{d2011|0,0,0}
44x,-z,y
-√2s+/2+i√2s-/2,i√2s+/2-√2s-/2
(
   1   0   0      0
   0   0  -1      0
   0   1   0      0
)
(
 -√2/2 i√2/2
 i√2/2 -√2/2
)
{d4+100|0,0,0}
45z,y,-x
-√2s+/2+√2s-/2,-√2s+/2-√2s-/2
(
   0   0   1      0
   0   1   0      0
  -1   0   0      0
)
(
 -√2/2  √2/2
 -√2/2 -√2/2
)
{d4+010|0,0,0}
46z,-y,x
i√2s+/2+i√2s-/2,i√2s+/2-i√2s-/2
(
   0   0   1      0
   0  -1   0      0
   1   0   0      0
)
(
  i√2/2  i√2/2
  i√2/2 -i√2/2
)
{d2101|0,0,0}
47-z,y,x
-√2s+/2-√2s-/2,√2s+/2-√2s-/2
(
   0   0  -1      0
   0   1   0      0
   1   0   0      0
)
(
 -√2/2 -√2/2
  √2/2 -√2/2
)
{d4-010|0,0,0}
48-z,-y,-x
-i√2s+/2+i√2s-/2,i√2s+/2+i√2s-/2
(
   0   0  -1      0
   0  -1   0      0
  -1   0   0      0
)
(
 -i√2/2  i√2/2
  i√2/2  i√2/2
)
{d2101|0,0,0}
(1/2,1/2,1/2)+set


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