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General Positions of the Group PC4/mbm (#127.397) [BNS setting]

127.397 P4/mbm.1'C[rP4/mmm] (UNI symbol)

To display the general positions in the OG setting, please follow this link: PP4'/mmm' ( #123.17.1015) [Transformation matrix]

Translation lattice generators: (1|1,0,0), (1|0,1,0), (1|0,0,1), (1|0,0,0)

Black-and-white lattice generators: (1|1,0,0), (1|0,1,0), (1|0,0,1), (1'|1/2,1/2,0)

N Standard/Default Setting
(x,y,z) form Matrix form Geom. interp. Seitz notation
1 x, y, z, +1
mx,my,mz
(
   1   0   0    0
   0   1   0    0
   0   0   1    0
)
 1 +1 { 1 | 0 }
2 -y, x, z, +1
-my,mx,mz
(
   0  -1   0    0
   1   0   0    0
   0   0   1    0
)
 4+ 0,0,z +1 { 4+001 | 0 }
3 y, -x, z, +1
my,-mx,mz
(
   0   1   0    0
  -1   0   0    0
   0   0   1    0
)
 4- 0,0,z +1 { 4-001 | 0 }
4 x+1/2, -y+1/2, -z, +1
mx,-my,-mz
(
   1   0   0   1/2
   0  -1   0   1/2
   0   0  -1    0
)
 2 (1/2,0,0) x,1/4,0 +1 { 2100 | 1/2 1/2 0 }
5 -x+1/2, y+1/2, -z, +1
-mx,my,-mz
(
  -1   0   0   1/2
   0   1   0   1/2
   0   0  -1    0
)
 2 (0,1/2,0) 1/4,y,0 +1 { 2010 | 1/2 1/2 0 }
6 -x, -y, z, +1
-mx,-my,mz
(
  -1   0   0    0
   0  -1   0    0
   0   0   1    0
)
 2 0,0,z +1 { 2001 | 0 }
7 y+1/2, x+1/2, -z, +1
my,mx,-mz
(
   0   1   0   1/2
   1   0   0   1/2
   0   0  -1    0
)
 2 (1/2,1/2,0) x,x,0 +1 { 2110 | 1/2 1/2 0 }
8 -y+1/2, -x+1/2, -z, +1
-my,-mx,-mz
(
   0  -1   0   1/2
  -1   0   0   1/2
   0   0  -1    0
)
 2 x,-x+1/2,0 +1 { 21-10 | 1/2 1/2 0 }
9 -x, -y, -z, +1
mx,my,mz
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
 -1 0,0,0 +1 { -1 | 0 }
10 y, -x, -z, +1
-my,mx,mz
(
   0   1   0    0
  -1   0   0    0
   0   0  -1    0
)
 -4+ 0,0,z 0,0,0 +1 { -4+001 | 0 }
11 -y, x, -z, +1
my,-mx,mz
(
   0  -1   0    0
   1   0   0    0
   0   0  -1    0
)
 -4- 0,0,z 0,0,0 +1 { -4-001 | 0 }
12 -x+1/2, y+1/2, z, +1
mx,-my,-mz
(
  -1   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)
 b 1/4,y,z +1 { m100 | 1/2 1/2 0 }
13 x+1/2, -y+1/2, z, +1
-mx,my,-mz
(
   1   0   0   1/2
   0  -1   0   1/2
   0   0   1    0
)
 a x,1/4,z +1 { m010 | 1/2 1/2 0 }
14 x, y, -z, +1
-mx,-my,mz
(
   1   0   0    0
   0   1   0    0
   0   0  -1    0
)
 m x,y,0 +1 { m001 | 0 }
15 -y+1/2, -x+1/2, z, +1
my,mx,-mz
(
   0  -1   0   1/2
  -1   0   0   1/2
   0   0   1    0
)
 m x+1/2,-x,z +1 { m110 | 1/2 1/2 0 }
16 y+1/2, x+1/2, z, +1
-my,-mx,-mz
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1    0
)
 g (1/2,1/2,0) x,x,z +1 { m1-10 | 1/2 1/2 0 }
17 x+1/2, y+1/2, z, -1
-mx,-my,-mz
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)'
 t (1/2,1/2,0) -1 { 1' | 1/2 1/2 0 }
18 -y+1/2, x+1/2, z, -1
my,-mx,-mz
(
   0  -1   0   1/2
   1   0   0   1/2
   0   0   1    0
)'
 4+ 0,1/2,z -1 { 4'+001 | 1/2 1/2 0 }
19 y+1/2, -x+1/2, z, -1
-my,mx,-mz
(
   0   1   0   1/2
  -1   0   0   1/2
   0   0   1    0
)'
 4- 1/2,0,z -1 { 4'-001 | 1/2 1/2 0 }
20 x, -y, -z, -1
-mx,my,mz
(
   1   0   0    0
   0  -1   0    0
   0   0  -1    0
)'
 2 x,0,0 -1 { 2'100 | 0 }
21 -x, y, -z, -1
mx,-my,mz
(
  -1   0   0    0
   0   1   0    0
   0   0  -1    0
)'
 2 0,y,0 -1 { 2'010 | 0 }
22 -x+1/2, -y+1/2, z, -1
mx,my,-mz
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0   1    0
)'
 2 1/4,1/4,z -1 { 2'001 | 1/2 1/2 0 }
23 y, x, -z, -1
-my,-mx,mz
(
   0   1   0    0
   1   0   0    0
   0   0  -1    0
)'
 2 x,x,0 -1 { 2'110 | 0 }
24 -y, -x, -z, -1
my,mx,mz
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1    0
)'
 2 x,-x,0 -1 { 2'1-10 | 0 }
25 -x+1/2, -y+1/2, -z, -1
-mx,-my,-mz
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1    0
)'
 -1 1/4,1/4,0 -1 { -1' | 1/2 1/2 0 }
26 y+1/2, -x+1/2, -z, -1
my,-mx,-mz
(
   0   1   0   1/2
  -1   0   0   1/2
   0   0  -1    0
)'
 -4+ 1/2,0,z 1/2,0,0 -1 { -4'+001 | 1/2 1/2 0 }
27 -y+1/2, x+1/2, -z, -1
-my,mx,-mz
(
   0  -1   0   1/2
   1   0   0   1/2
   0   0  -1    0
)'
 -4- 0,1/2,z 0,1/2,0 -1 { -4'-001 | 1/2 1/2 0 }
28 -x, y, z, -1
-mx,my,mz
(
  -1   0   0    0
   0   1   0    0
   0   0   1    0
)'
 m 0,y,z -1 { m'100 | 0 }
29 x, -y, z, -1
mx,-my,mz
(
   1   0   0    0
   0  -1   0    0
   0   0   1    0
)'
 m x,0,z -1 { m'010 | 0 }
30 x+1/2, y+1/2, -z, -1
mx,my,-mz
(
   1   0   0   1/2
   0   1   0   1/2
   0   0  -1    0
)'
 n (1/2,1/2,0) x,y,0 -1 { m'001 | 1/2 1/2 0 }
31 -y, -x, z, -1
-my,-mx,mz
(
   0  -1   0    0
  -1   0   0    0
   0   0   1    0
)'
 m x,-x,z -1 { m'110 | 0 }
32 y, x, z, -1
my,mx,mz
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)'
 m x,x,z -1 { m'1-10 | 0 }

Go to the list of the Wyckoff Positions of the Group PC4/mbm (#127.397)
Go to the Systematic Absences for the Group PC4/mbm (#127.397)

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