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Symmetry operations of the Double Space Group Fd-3m (No. 227)


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,1/4-y,1/2+z
-is+,is-
(
  -1   0   0    3/4
   0  -1   0    1/4
   0   0   1    1/2
)
(
 -i  0
  0  i
)
{2001|3/4,1/4,1/2}
31/4-x,1/2+y,3/4-z
-s-,s+
(
  -1   0   0    1/4
   0   1   0    1/2
   0   0  -1    3/4
)
(
  0 -1
  1  0
)
{2010|1/4,1/2,3/4}
41/2+x,3/4-y,1/4-z
-is-,-is+
(
   1   0   0    1/2
   0  -1   0    3/4
   0   0  -1    1/4
)
(
  0 -i
 -i  0
)
{2100|1/2,3/4,1/4}
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}
61/2+z,3/4-x,1/4-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    3/4
   0  -1   0    1/4
)
(
  (1+i)/2 -(1-i)/2
  (1+i)/2  (1-i)/2
)
{3+111|1/2,3/4,1/4}
73/4-z,1/4-x,1/2+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    1/4
   0   1   0    1/2
)
(
  (1+i)/2  (1-i)/2
 -(1+i)/2  (1-i)/2
)
{3+111|3/4,1/4,1/2}
81/4-z,1/2+x,3/4-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    1/2
   0  -1   0    3/4
)
(
  (1-i)/2  (1+i)/2
 -(1-i)/2  (1+i)/2
)
{3+111|1/4,1/2,3/4}
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}
101/4-y,1/2+z,3/4-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    1/2
  -1   0   0    3/4
)
(
  (1-i)/2 -(1-i)/2
  (1+i)/2  (1+i)/2
)
{3-111|1/4,1/2,3/4}
111/2+y,3/4-z,1/4-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    3/4
  -1   0   0    1/4
)
(
  (1+i)/2 -(1+i)/2
  (1-i)/2  (1-i)/2
)
{3-111|1/2,3/4,1/4}
123/4-y,1/4-z,1/2+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    1/4
   1   0   0    1/2
)
(
  (1-i)/2  (1-i)/2
 -(1+i)/2  (1+i)/2
)
{3-111|3/4,1/4,1/2}
133/4+y,1/4+x,1/2-z
-(1+i)√2s-/2,(1-i)√2s+/2
(
   0   1   0    3/4
   1   0   0    1/4
   0   0  -1    1/2
)
(
  0 -(1+i)√2/2
  (1-i)√2/2  0
)
{2110|3/4,1/4,1/2}
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}
151/4+y,1/2-x,3/4+z
(1+i)√2s+/2,(1-i)√2s-/2
(
   0   1   0    1/4
  -1   0   0    1/2
   0   0   1    3/4
)
(
 (1+i)√2/2  0
  0 (1-i)√2/2
)
{4-001|1/4,1/2,3/4}
161/2-y,3/4+x,1/4+z
(1-i)√2s+/2,(1+i)√2s-/2
(
   0  -1   0    1/2
   1   0   0    3/4
   0   0   1    1/4
)
(
 (1-i)√2/2  0
  0 (1+i)√2/2
)
{4+001|1/2,3/4,1/4}
173/4+x,1/4+z,1/2-y
√2s+/2+i√2s-/2,i√2s+/2+√2s-/2
(
   1   0   0    3/4
   0   0   1    1/4
   0  -1   0    1/2
)
(
  √2/2 i√2/2
 i√2/2  √2/2
)
{4-100|3/4,1/4,1/2}
181/2-x,3/4+z,1/4+y
i√2s+/2+√2s-/2,-√2s+/2-i√2s-/2
(
  -1   0   0    1/2
   0   0   1    3/4
   0   1   0    1/4
)
(
  i√2/2  √2/2
  -√2/2 -i√2/2
)
{2011|1/2,3/4,1/4}
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}
201/4+x,1/2-z,3/4+y
√2s+/2-i√2s-/2,-i√2s+/2+√2s-/2
(
   1   0   0    1/4
   0   0  -1    1/2
   0   1   0    3/4
)
(
  √2/2 -i√2/2
 -i√2/2  √2/2
)
{4+100|1/4,1/2,3/4}
213/4+z,1/4+y,1/2-x
√2s+/2-√2s-/2,√2s+/2+√2s-/2
(
   0   0   1    3/4
   0   1   0    1/4
  -1   0   0    1/2
)
(
  √2/2 -√2/2
  √2/2  √2/2
)
{4+010|3/4,1/4,1/2}
221/4+z,1/2-y,3/4+x
-i√2s+/2-i√2s-/2,-i√2s+/2+i√2s-/2
(
   0   0   1    1/4
   0  -1   0    1/2
   1   0   0    3/4
)
(
 -i√2/2 -i√2/2
 -i√2/2  i√2/2
)
{2101|1/4,1/2,3/4}
231/2-z,3/4+y,1/4+x
√2s+/2+√2s-/2,-√2s+/2+√2s-/2
(
   0   0  -1    1/2
   0   1   0    3/4
   1   0   0    1/4
)
(
  √2/2  √2/2
 -√2/2  √2/2
)
{4-010|1/2,3/4,1/4}
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}
25-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}
261/4+x,3/4+y,1/2-z
-is+,is-
(
   1   0   0    1/4
   0   1   0    3/4
   0   0  -1    1/2
)
(
 -i  0
  0  i
)
{m001|1/4,3/4,1/2}
273/4+x,1/2-y,1/4+z
-s-,s+
(
   1   0   0    3/4
   0  -1   0    1/2
   0   0   1    1/4
)
(
  0 -1
  1  0
)
{m010|3/4,1/2,1/4}
281/2-x,1/4+y,3/4+z
-is-,-is+
(
  -1   0   0    1/2
   0   1   0    1/4
   0   0   1    3/4
)
(
  0 -i
 -i  0
)
{m100|1/2,1/4,3/4}
29-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}
301/2-z,1/4+x,3/4+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    1/4
   0   1   0    3/4
)
(
  (1+i)/2 -(1-i)/2
  (1+i)/2  (1-i)/2
)
{3+111|1/2,1/4,3/4}
311/4+z,3/4+x,1/2-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    3/4
   0  -1   0    1/2
)
(
  (1+i)/2  (1-i)/2
 -(1+i)/2  (1-i)/2
)
{3+111|1/4,3/4,1/2}
323/4+z,1/2-x,1/4+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    1/2
   0   1   0    1/4
)
(
  (1-i)/2  (1+i)/2
 -(1-i)/2  (1+i)/2
)
{3+111|3/4,1/2,1/4}
33-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}
343/4+y,1/2-z,1/4+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    1/2
   1   0   0    1/4
)
(
  (1-i)/2 -(1-i)/2
  (1+i)/2  (1+i)/2
)
{3-111|3/4,1/2,1/4}
351/2-y,1/4+z,3/4+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    1/4
   1   0   0    3/4
)
(
  (1+i)/2 -(1+i)/2
  (1-i)/2  (1-i)/2
)
{3-111|1/2,1/4,3/4}
361/4+y,3/4+z,1/2-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    3/4
  -1   0   0    1/2
)
(
  (1-i)/2  (1-i)/2
 -(1+i)/2  (1+i)/2
)
{3-111|1/4,3/4,1/2}
371/4-y,3/4-x,1/2+z
-(1+i)√2s-/2,(1-i)√2s+/2
(
   0  -1   0    1/4
  -1   0   0    3/4
   0   0   1    1/2
)
(
  0 -(1+i)√2/2
  (1-i)√2/2  0
)
{m110|1/4,3/4,1/2}
38y,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
)
{m110|0,0,0}
393/4-y,1/2+x,1/4-z
(1+i)√2s+/2,(1-i)√2s-/2
(
   0  -1   0    3/4
   1   0   0    1/2
   0   0  -1    1/4
)
(
 (1+i)√2/2  0
  0 (1-i)√2/2
)
{4-001|3/4,1/2,1/4}
401/2+y,1/4-x,3/4-z
(1-i)√2s+/2,(1+i)√2s-/2
(
   0   1   0    1/2
  -1   0   0    1/4
   0   0  -1    3/4
)
(
 (1-i)√2/2  0
  0 (1+i)√2/2
)
{4+001|1/2,1/4,3/4}
411/4-x,3/4-z,1/2+y
√2s+/2+i√2s-/2,i√2s+/2+√2s-/2
(
  -1   0   0    1/4
   0   0  -1    3/4
   0   1   0    1/2
)
(
  √2/2 i√2/2
 i√2/2  √2/2
)
{4-100|1/4,3/4,1/2}
421/2+x,1/4-z,3/4-y
i√2s+/2+√2s-/2,-√2s+/2-i√2s-/2
(
   1   0   0    1/2
   0   0  -1    1/4
   0  -1   0    3/4
)
(
  i√2/2  √2/2
  -√2/2 -i√2/2
)
{m011|1/2,1/4,3/4}
43x,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
)
{m011|0,0,0}
443/4-x,1/2+z,1/4-y
√2s+/2-i√2s-/2,-i√2s+/2+√2s-/2
(
  -1   0   0    3/4
   0   0   1    1/2
   0  -1   0    1/4
)
(
  √2/2 -i√2/2
 -i√2/2  √2/2
)
{4+100|3/4,1/2,1/4}
451/4-z,3/4-y,1/2+x
√2s+/2-√2s-/2,√2s+/2+√2s-/2
(
   0   0  -1    1/4
   0  -1   0    3/4
   1   0   0    1/2
)
(
  √2/2 -√2/2
  √2/2  √2/2
)
{4+010|1/4,3/4,1/2}
463/4-z,1/2+y,1/4-x
-i√2s+/2-i√2s-/2,-i√2s+/2+i√2s-/2
(
   0   0  -1    3/4
   0   1   0    1/2
  -1   0   0    1/4
)
(
 -i√2/2 -i√2/2
 -i√2/2  i√2/2
)
{m101|3/4,1/2,1/4}
471/2+z,1/4-y,3/4-x
√2s+/2+√2s-/2,-√2s+/2+√2s-/2
(
   0   0   1    1/2
   0  -1   0    1/4
  -1   0   0    3/4
)
(
  √2/2  √2/2
 -√2/2  √2/2
)
{4-010|1/2,1/4,3/4}
48z,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
)
{m101|0,0,0}
49x,y,z
-s+,-s-
(
   1   0   0      0
   0   1   0      0
   0   0   1      0
)
(
 -1  0
  0 -1
)
{d1|0,0,0}
503/4-x,1/4-y,1/2+z
is+,-is-
(
  -1   0   0    3/4
   0  -1   0    1/4
   0   0   1    1/2
)
(
  i  0
  0 -i
)
{d2001|3/4,1/4,1/2}
511/4-x,1/2+y,3/4-z
s-,-s+
(
  -1   0   0    1/4
   0   1   0    1/2
   0   0  -1    3/4
)
(
  0  1
 -1  0
)
{d2010|1/4,1/2,3/4}
521/2+x,3/4-y,1/4-z
is-,is+
(
   1   0   0    1/2
   0  -1   0    3/4
   0   0  -1    1/4
)
(
 0 i
 i 0
)
{d2100|1/2,3/4,1/4}
53z,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}
541/2+z,3/4-x,1/4-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    3/4
   0  -1   0    1/4
)
(
 -(1+i)/2  (1-i)/2
 -(1+i)/2 -(1-i)/2
)
{d3+111|1/2,3/4,1/4}
553/4-z,1/4-x,1/2+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    1/4
   0   1   0    1/2
)
(
 -(1+i)/2 -(1-i)/2
  (1+i)/2 -(1-i)/2
)
{d3+111|3/4,1/4,1/2}
561/4-z,1/2+x,3/4-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    1/2
   0  -1   0    3/4
)
(
 -(1-i)/2 -(1+i)/2
  (1-i)/2 -(1+i)/2
)
{d3+111|1/4,1/2,3/4}
57y,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}
581/4-y,1/2+z,3/4-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    1/2
  -1   0   0    3/4
)
(
 -(1-i)/2  (1-i)/2
 -(1+i)/2 -(1+i)/2
)
{d3-111|1/4,1/2,3/4}
591/2+y,3/4-z,1/4-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    3/4
  -1   0   0    1/4
)
(
 -(1+i)/2  (1+i)/2
 -(1-i)/2 -(1-i)/2
)
{d3-111|1/2,3/4,1/4}
603/4-y,1/4-z,1/2+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    1/4
   1   0   0    1/2
)
(
 -(1-i)/2 -(1-i)/2
  (1+i)/2 -(1+i)/2
)
{d3-111|3/4,1/4,1/2}
613/4+y,1/4+x,1/2-z
(1+i)√2s-/2,-(1-i)√2s+/2
(
   0   1   0    3/4
   1   0   0    1/4
   0   0  -1    1/2
)
(
  0  (1+i)√2/2
 -(1-i)√2/2  0
)
{d2110|3/4,1/4,1/2}
62-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}
631/4+y,1/2-x,3/4+z
-(1+i)√2s+/2,-(1-i)√2s-/2
(
   0   1   0    1/4
  -1   0   0    1/2
   0   0   1    3/4
)
(
 -(1+i)√2/2  0
  0 -(1-i)√2/2
)
{d4-001|1/4,1/2,3/4}
641/2-y,3/4+x,1/4+z
-(1-i)√2s+/2,-(1+i)√2s-/2
(
   0  -1   0    1/2
   1   0   0    3/4
   0   0   1    1/4
)
(
 -(1-i)√2/2  0
  0 -(1+i)√2/2
)
{d4+001|1/2,3/4,1/4}
653/4+x,1/4+z,1/2-y
-√2s+/2-i√2s-/2,-i√2s+/2-√2s-/2
(
   1   0   0    3/4
   0   0   1    1/4
   0  -1   0    1/2
)
(
  -√2/2 -i√2/2
 -i√2/2  -√2/2
)
{d4-100|3/4,1/4,1/2}
661/2-x,3/4+z,1/4+y
-i√2s+/2-√2s-/2,√2s+/2+i√2s-/2
(
  -1   0   0    1/2
   0   0   1    3/4
   0   1   0    1/4
)
(
 -i√2/2  -√2/2
  √2/2  i√2/2
)
{d2011|1/2,3/4,1/4}
67-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}
681/4+x,1/2-z,3/4+y
-√2s+/2+i√2s-/2,i√2s+/2-√2s-/2
(
   1   0   0    1/4
   0   0  -1    1/2
   0   1   0    3/4
)
(
 -√2/2 i√2/2
 i√2/2 -√2/2
)
{d4+100|1/4,1/2,3/4}
693/4+z,1/4+y,1/2-x
-√2s+/2+√2s-/2,-√2s+/2-√2s-/2
(
   0   0   1    3/4
   0   1   0    1/4
  -1   0   0    1/2
)
(
 -√2/2  √2/2
 -√2/2 -√2/2
)
{d4+010|3/4,1/4,1/2}
701/4+z,1/2-y,3/4+x
i√2s+/2+i√2s-/2,i√2s+/2-i√2s-/2
(
   0   0   1    1/4
   0  -1   0    1/2
   1   0   0    3/4
)
(
  i√2/2  i√2/2
  i√2/2 -i√2/2
)
{d2101|1/4,1/2,3/4}
711/2-z,3/4+y,1/4+x
-√2s+/2-√2s-/2,√2s+/2-√2s-/2
(
   0   0  -1    1/2
   0   1   0    3/4
   1   0   0    1/4
)
(
 -√2/2 -√2/2
  √2/2 -√2/2
)
{d4-010|1/2,3/4,1/4}
72-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}
73-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}
741/4+x,3/4+y,1/2-z
is+,-is-
(
   1   0   0    1/4
   0   1   0    3/4
   0   0  -1    1/2
)
(
  i  0
  0 -i
)
{dm001|1/4,3/4,1/2}
753/4+x,1/2-y,1/4+z
s-,-s+
(
   1   0   0    3/4
   0  -1   0    1/2
   0   0   1    1/4
)
(
  0  1
 -1  0
)
{dm010|3/4,1/2,1/4}
761/2-x,1/4+y,3/4+z
is-,is+
(
  -1   0   0    1/2
   0   1   0    1/4
   0   0   1    3/4
)
(
 0 i
 i 0
)
{dm100|1/2,1/4,3/4}
77-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}
781/2-z,1/4+x,3/4+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    1/4
   0   1   0    3/4
)
(
 -(1+i)/2  (1-i)/2
 -(1+i)/2 -(1-i)/2
)
{d3+111|1/2,1/4,3/4}
791/4+z,3/4+x,1/2-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    3/4
   0  -1   0    1/2
)
(
 -(1+i)/2 -(1-i)/2
  (1+i)/2 -(1-i)/2
)
{d3+111|1/4,3/4,1/2}
803/4+z,1/2-x,1/4+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    1/2
   0   1   0    1/4
)
(
 -(1-i)/2 -(1+i)/2
  (1-i)/2 -(1+i)/2
)
{d3+111|3/4,1/2,1/4}
81-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}
823/4+y,1/2-z,1/4+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    1/2
   1   0   0    1/4
)
(
 -(1-i)/2  (1-i)/2
 -(1+i)/2 -(1+i)/2
)
{d3-111|3/4,1/2,1/4}
831/2-y,1/4+z,3/4+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    1/4
   1   0   0    3/4
)
(
 -(1+i)/2  (1+i)/2
 -(1-i)/2 -(1-i)/2
)
{d3-111|1/2,1/4,3/4}
841/4+y,3/4+z,1/2-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    3/4
  -1   0   0    1/2
)
(
 -(1-i)/2 -(1-i)/2
  (1+i)/2 -(1+i)/2
)
{d3-111|1/4,3/4,1/2}
851/4-y,3/4-x,1/2+z
(1+i)√2s-/2,-(1-i)√2s+/2
(
   0  -1   0    1/4
  -1   0   0    3/4
   0   0   1    1/2
)
(
  0  (1+i)√2/2
 -(1-i)√2/2  0
)
{dm110|1/4,3/4,1/2}
86y,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
)
{dm110|0,0,0}
873/4-y,1/2+x,1/4-z
-(1+i)√2s+/2,-(1-i)√2s-/2
(
   0  -1   0    3/4
   1   0   0    1/2
   0   0  -1    1/4
)
(
 -(1+i)√2/2  0
  0 -(1-i)√2/2
)
{d4-001|3/4,1/2,1/4}
881/2+y,1/4-x,3/4-z
-(1-i)√2s+/2,-(1+i)√2s-/2
(
   0   1   0    1/2
  -1   0   0    1/4
   0   0  -1    3/4
)
(
 -(1-i)√2/2  0
  0 -(1+i)√2/2
)
{d4+001|1/2,1/4,3/4}
891/4-x,3/4-z,1/2+y
-√2s+/2-i√2s-/2,-i√2s+/2-√2s-/2
(
  -1   0   0    1/4
   0   0  -1    3/4
   0   1   0    1/2
)
(
  -√2/2 -i√2/2
 -i√2/2  -√2/2
)
{d4-100|1/4,3/4,1/2}
901/2+x,1/4-z,3/4-y
-i√2s+/2-√2s-/2,√2s+/2+i√2s-/2
(
   1   0   0    1/2
   0   0  -1    1/4
   0  -1   0    3/4
)
(
 -i√2/2  -√2/2
  √2/2  i√2/2
)
{dm011|1/2,1/4,3/4}
91x,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
)
{dm011|0,0,0}
923/4-x,1/2+z,1/4-y
-√2s+/2+i√2s-/2,i√2s+/2-√2s-/2
(
  -1   0   0    3/4
   0   0   1    1/2
   0  -1   0    1/4
)
(
 -√2/2 i√2/2
 i√2/2 -√2/2
)
{d4+100|3/4,1/2,1/4}
931/4-z,3/4-y,1/2+x
-√2s+/2+√2s-/2,-√2s+/2-√2s-/2
(
   0   0  -1    1/4
   0  -1   0    3/4
   1   0   0    1/2
)
(
 -√2/2  √2/2
 -√2/2 -√2/2
)
{d4+010|1/4,3/4,1/2}
943/4-z,1/2+y,1/4-x
i√2s+/2+i√2s-/2,i√2s+/2-i√2s-/2
(
   0   0  -1    3/4
   0   1   0    1/2
  -1   0   0    1/4
)
(
  i√2/2  i√2/2
  i√2/2 -i√2/2
)
{dm101|3/4,1/2,1/4}
951/2+z,1/4-y,3/4-x
-√2s+/2-√2s-/2,√2s+/2-√2s-/2
(
   0   0   1    1/2
   0  -1   0    1/4
  -1   0   0    3/4
)
(
 -√2/2 -√2/2
  √2/2 -√2/2
)
{d4-010|1/2,1/4,3/4}
96z,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
)
{dm101|0,0,0}
(0,1/2,1/2)+set
(1/2,0,1/2)+set
(1/2,1/2,0)+set


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