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Symmetry operations of the Double Space Group P-421m (No. 113)


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}
3y,-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}
4-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}
51/2-x,1/2+y,-z
-s-,s+
(
  -1   0   0    1/2
   0   1   0    1/2
   0   0  -1      0
)
(
0 -1
1 0
)
{2010|1/2,1/2,0}
61/2+x,1/2-y,-z
-is-,-is+
(
   1   0   0    1/2
   0  -1   0    1/2
   0   0  -1      0
)
(
0 -i
-i 0
)
{2100|1/2,1/2,0}
71/2-y,1/2-x,z
-(1+i)2s-/2,(1-i)2s+/2
(
   0  -1   0    1/2
  -1   0   0    1/2
   0   0   1      0
)
(
0 -(1+i)2/2
(1-i)2/2 0
)
{m110|1/2,1/2,0}
81/2+y,1/2+x,z
-(1-i)2s-/2,(1+i)2s+/2
(
   0   1   0    1/2
   1   0   0    1/2
   0   0   1      0
)
(
0 -(1-i)2/2
(1+i)2/2 0
)
{m110|1/2,1/2,0}
9x,y,z
-s+,-s-
(
   1   0   0      0
   0   1   0      0
   0   0   1      0
)
(
-1 0
0 -1
)
{d1|0,0,0}
10-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}
11y,-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}
12-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}
131/2-x,1/2+y,-z
s-,-s+
(
  -1   0   0    1/2
   0   1   0    1/2
   0   0  -1      0
)
(
0 1
-1 0
)
{d2010|1/2,1/2,0}
141/2+x,1/2-y,-z
is-,is+
(
   1   0   0    1/2
   0  -1   0    1/2
   0   0  -1      0
)
(
0 i
i 0
)
{d2100|1/2,1/2,0}
151/2-y,1/2-x,z
(1+i)2s-/2,-(1-i)2s+/2
(
   0  -1   0    1/2
  -1   0   0    1/2
   0   0   1      0
)
(
0 (1+i)2/2
-(1-i)2/2 0
)
{dm110|1/2,1/2,0}
161/2+y,1/2+x,z
(1-i)2s-/2,-(1+i)2s+/2
(
   0   1   0    1/2
   1   0   0    1/2
   0   0   1      0
)
(
0 (1-i)2/2
-(1+i)2/2 0
)
{dm110|1/2,1/2,0}


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