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Symmetry operations of the Double Space Group P6/mmm (No. 191)


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}
4-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}
5y,-x+y,z
-(i-3)s+/2,(i+3)s-/2
(
   0   1   0      0
  -1   1   0      0
   0   0   1      0
)
(
-(i-3)/2 0
0 (i+3)/2
)
{6-001|0,0,0}
6x-y,x,z
(i+3)s+/2,-(i-3)s-/2
(
   1  -1   0      0
   1   0   0      0
   0   0   1      0
)
(
(i+3)/2 0
0 -(i-3)/2
)
{6+001|0,0,0}
7y,x,-z
-(1+i3)s-/2,(1-i3)s+/2
(
   0   1   0      0
   1   0   0      0
   0   0  -1      0
)
(
0 -(1+i3)/2
(1-i3)/2 0
)
{2110|0,0,0}
8x-y,-y,-z
-s-,s+
(
   1  -1   0      0
   0  -1   0      0
   0   0  -1      0
)
(
0 -1
1 0
)
{2100|0,0,0}
9-x,-x+y,-z
-(1-i3)s-/2,(1+i3)s+/2
(
  -1   0   0      0
  -1   1   0      0
   0   0  -1      0
)
(
0 -(1-i3)/2
(1+i3)/2 0
)
{2010|0,0,0}
10-y,-x,-z
(i-3)s-/2,(i+3)s+/2
(
   0  -1   0      0
  -1   0   0      0
   0   0  -1      0
)
(
0 (i-3)/2
(i+3)/2 0
)
{2110|0,0,0}
11-x+y,y,-z
-is-,-is+
(
  -1   1   0      0
   0   1   0      0
   0   0  -1      0
)
(
0 -i
-i 0
)
{2120|0,0,0}
12x,x-y,-z
(i+3)s-/2,(i-3)s+/2
(
   1   0   0      0
   1  -1   0      0
   0   0  -1      0
)
(
0 (i+3)/2
(i-3)/2 0
)
{2210|0,0,0}
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}
14y,-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}
15x-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}
16x,y,-z
-is+,is-
(
   1   0   0      0
   0   1   0      0
   0   0  -1      0
)
(
-i 0
0 i
)
{m001|0,0,0}
17-y,x-y,-z
-(i-3)s+/2,(i+3)s-/2
(
   0  -1   0      0
   1  -1   0      0
   0   0  -1      0
)
(
-(i-3)/2 0
0 (i+3)/2
)
{6-001|0,0,0}
18-x+y,-x,-z
(i+3)s+/2,-(i-3)s-/2
(
  -1   1   0      0
  -1   0   0      0
   0   0  -1      0
)
(
(i+3)/2 0
0 -(i-3)/2
)
{6+001|0,0,0}
19-y,-x,z
-(1+i3)s-/2,(1-i3)s+/2
(
   0  -1   0      0
  -1   0   0      0
   0   0   1      0
)
(
0 -(1+i3)/2
(1-i3)/2 0
)
{m110|0,0,0}
20-x+y,y,z
-s-,s+
(
  -1   1   0      0
   0   1   0      0
   0   0   1      0
)
(
0 -1
1 0
)
{m100|0,0,0}
21x,x-y,z
-(1-i3)s-/2,(1+i3)s+/2
(
   1   0   0      0
   1  -1   0      0
   0   0   1      0
)
(
0 -(1-i3)/2
(1+i3)/2 0
)
{m010|0,0,0}
22y,x,z
(i-3)s-/2,(i+3)s+/2
(
   0   1   0      0
   1   0   0      0
   0   0   1      0
)
(
0 (i-3)/2
(i+3)/2 0
)
{m110|0,0,0}
23x-y,-y,z
-is-,-is+
(
   1  -1   0      0
   0  -1   0      0
   0   0   1      0
)
(
0 -i
-i 0
)
{m120|0,0,0}
24-x,-x+y,z
(i+3)s-/2,(i-3)s+/2
(
  -1   0   0      0
  -1   1   0      0
   0   0   1      0
)
(
0 (i+3)/2
(i-3)/2 0
)
{m210|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-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}
27-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}
28-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}
29y,-x+y,z
(i-3)s+/2,-(i+3)s-/2
(
   0   1   0      0
  -1   1   0      0
   0   0   1      0
)
(
(i-3)/2 0
0 -(i+3)/2
)
{d6-001|0,0,0}
30x-y,x,z
-(i+3)s+/2,(i-3)s-/2
(
   1  -1   0      0
   1   0   0      0
   0   0   1      0
)
(
-(i+3)/2 0
0 (i-3)/2
)
{d6+001|0,0,0}
31y,x,-z
(1+i3)s-/2,-(1-i3)s+/2
(
   0   1   0      0
   1   0   0      0
   0   0  -1      0
)
(
0 (1+i3)/2
-(1-i3)/2 0
)
{d2110|0,0,0}
32x-y,-y,-z
s-,-s+
(
   1  -1   0      0
   0  -1   0      0
   0   0  -1      0
)
(
0 1
-1 0
)
{d2100|0,0,0}
33-x,-x+y,-z
(1-i3)s-/2,-(1+i3)s+/2
(
  -1   0   0      0
  -1   1   0      0
   0   0  -1      0
)
(
0 (1-i3)/2
-(1+i3)/2 0
)
{d2010|0,0,0}
34-y,-x,-z
-(i-3)s-/2,-(i+3)s+/2
(
   0  -1   0      0
  -1   0   0      0
   0   0  -1      0
)
(
0 -(i-3)/2
-(i+3)/2 0
)
{d2110|0,0,0}
35-x+y,y,-z
is-,is+
(
  -1   1   0      0
   0   1   0      0
   0   0  -1      0
)
(
0 i
i 0
)
{d2120|0,0,0}
36x,x-y,-z
-(i+3)s-/2,-(i-3)s+/2
(
   1   0   0      0
   1  -1   0      0
   0   0  -1      0
)
(
0 -(i+3)/2
-(i-3)/2 0
)
{d2210|0,0,0}
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}
38y,-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}
39x-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}
40x,y,-z
is+,-is-
(
   1   0   0      0
   0   1   0      0
   0   0  -1      0
)
(
i 0
0 -i
)
{dm001|0,0,0}
41-y,x-y,-z
(i-3)s+/2,-(i+3)s-/2
(
   0  -1   0      0
   1  -1   0      0
   0   0  -1      0
)
(
(i-3)/2 0
0 -(i+3)/2
)
{d6-001|0,0,0}
42-x+y,-x,-z
-(i+3)s+/2,(i-3)s-/2
(
  -1   1   0      0
  -1   0   0      0
   0   0  -1      0
)
(
-(i+3)/2 0
0 (i-3)/2
)
{d6+001|0,0,0}
43-y,-x,z
(1+i3)s-/2,-(1-i3)s+/2
(
   0  -1   0      0
  -1   0   0      0
   0   0   1      0
)
(
0 (1+i3)/2
-(1-i3)/2 0
)
{dm110|0,0,0}
44-x+y,y,z
s-,-s+
(
  -1   1   0      0
   0   1   0      0
   0   0   1      0
)
(
0 1
-1 0
)
{dm100|0,0,0}
45x,x-y,z
(1-i3)s-/2,-(1+i3)s+/2
(
   1   0   0      0
   1  -1   0      0
   0   0   1      0
)
(
0 (1-i3)/2
-(1+i3)/2 0
)
{dm010|0,0,0}
46y,x,z
-(i-3)s-/2,-(i+3)s+/2
(
   0   1   0      0
   1   0   0      0
   0   0   1      0
)
(
0 -(i-3)/2
-(i+3)/2 0
)
{dm110|0,0,0}
47x-y,-y,z
is-,is+
(
   1  -1   0      0
   0  -1   0      0
   0   0   1      0
)
(
0 i
i 0
)
{dm120|0,0,0}
48-x,-x+y,z
-(i+3)s-/2,-(i-3)s+/2
(
  -1   0   0      0
  -1   1   0      0
   0   0   1      0
)
(
0 -(i+3)/2
-(i-3)/2 0
)
{dm210|0,0,0}


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