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Symmetry operations of the Double Space Group R-3c (No. 167)


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-y,x-y,z
(1+i3)s+/2,(1-i3)s-/2
(
   0  -1   0      0
   1  -1   0      0
   0   0   1      0
)
(
(1+i3)/2 0
0 (1-i3)/2
)
{3+001|0,0,0}
3-x+y,-x,z
(1-i3)s+/2,(1+i3)s-/2
(
  -1   1   0      0
  -1   0   0      0
   0   0   1      0
)
(
(1-i3)/2 0
0 (1+i3)/2
)
{3-001|0,0,0}
4y,x,1/2-z
-(1+i3)s-/2,(1-i3)s+/2
(
   0   1   0      0
   1   0   0      0
   0   0  -1    1/2
)
(
0 -(1+i3)/2
(1-i3)/2 0
)
{2110|0,0,1/2}
5x-y,-y,1/2-z
-s-,s+
(
   1  -1   0      0
   0  -1   0      0
   0   0  -1    1/2
)
(
0 -1
1 0
)
{2100|0,0,1/2}
6-x,-x+y,1/2-z
-(1-i3)s-/2,(1+i3)s+/2
(
  -1   0   0      0
  -1   1   0      0
   0   0  -1    1/2
)
(
0 -(1-i3)/2
(1+i3)/2 0
)
{2010|0,0,1/2}
7-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}
8y,-x+y,-z
(1+i3)s+/2,(1-i3)s-/2
(
   0   1   0      0
  -1   1   0      0
   0   0  -1      0
)
(
(1+i3)/2 0
0 (1-i3)/2
)
{3+001|0,0,0}
9x-y,x,-z
(1-i3)s+/2,(1+i3)s-/2
(
   1  -1   0      0
   1   0   0      0
   0   0  -1      0
)
(
(1-i3)/2 0
0 (1+i3)/2
)
{3-001|0,0,0}
10-y,-x,1/2+z
-(1+i3)s-/2,(1-i3)s+/2
(
   0  -1   0      0
  -1   0   0      0
   0   0   1    1/2
)
(
0 -(1+i3)/2
(1-i3)/2 0
)
{m110|0,0,1/2}
11-x+y,y,1/2+z
-s-,s+
(
  -1   1   0      0
   0   1   0      0
   0   0   1    1/2
)
(
0 -1
1 0
)
{m100|0,0,1/2}
12x,x-y,1/2+z
-(1-i3)s-/2,(1+i3)s+/2
(
   1   0   0      0
   1  -1   0      0
   0   0   1    1/2
)
(
0 -(1-i3)/2
(1+i3)/2 0
)
{m010|0,0,1/2}
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}
14-y,x-y,z
-(1+i3)s+/2,-(1-i3)s-/2
(
   0  -1   0      0
   1  -1   0      0
   0   0   1      0
)
(
-(1+i3)/2 0
0 -(1-i3)/2
)
{d3+001|0,0,0}
15-x+y,-x,z
-(1-i3)s+/2,-(1+i3)s-/2
(
  -1   1   0      0
  -1   0   0      0
   0   0   1      0
)
(
-(1-i3)/2 0
0 -(1+i3)/2
)
{d3-001|0,0,0}
16y,x,1/2-z
(1+i3)s-/2,-(1-i3)s+/2
(
   0   1   0      0
   1   0   0      0
   0   0  -1    1/2
)
(
0 (1+i3)/2
-(1-i3)/2 0
)
{d2110|0,0,1/2}
17x-y,-y,1/2-z
s-,-s+
(
   1  -1   0      0
   0  -1   0      0
   0   0  -1    1/2
)
(
0 1
-1 0
)
{d2100|0,0,1/2}
18-x,-x+y,1/2-z
(1-i3)s-/2,-(1+i3)s+/2
(
  -1   0   0      0
  -1   1   0      0
   0   0  -1    1/2
)
(
0 (1-i3)/2
-(1+i3)/2 0
)
{d2010|0,0,1/2}
19-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}
20y,-x+y,-z
-(1+i3)s+/2,-(1-i3)s-/2
(
   0   1   0      0
  -1   1   0      0
   0   0  -1      0
)
(
-(1+i3)/2 0
0 -(1-i3)/2
)
{d3+001|0,0,0}
21x-y,x,-z
-(1-i3)s+/2,-(1+i3)s-/2
(
   1  -1   0      0
   1   0   0      0
   0   0  -1      0
)
(
-(1-i3)/2 0
0 -(1+i3)/2
)
{d3-001|0,0,0}
22-y,-x,1/2+z
(1+i3)s-/2,-(1-i3)s+/2
(
   0  -1   0      0
  -1   0   0      0
   0   0   1    1/2
)
(
0 (1+i3)/2
-(1-i3)/2 0
)
{dm110|0,0,1/2}
23-x+y,y,1/2+z
s-,-s+
(
  -1   1   0      0
   0   1   0      0
   0   0   1    1/2
)
(
0 1
-1 0
)
{dm100|0,0,1/2}
24x,x-y,1/2+z
(1-i3)s-/2,-(1+i3)s+/2
(
   1   0   0      0
   1  -1   0      0
   0   0   1    1/2
)
(
0 (1-i3)/2
-(1+i3)/2 0
)
{dm010|0,0,1/2}
(2/3,1/3,1/3)+set
(1/3,2/3,2/3)+set


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