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General Positions of the Group I4/mm'm' (#139.537)
139.537 I4/mm'm' (UNI symbol)

For this space group, BNS and OG settings coincide.
Its label in the OG setting is given as: I4/mm'm' (#139.7.1185)

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, -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 }
5 -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 }
6 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 }
7 -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 }
8 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 }
9 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 }
10 -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 }
11 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 }
12 -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 }
13 -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 }
14 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 }
15 -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 }
16 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 }
17 x+1/2, y+1/2, z+1/2, +1
mx,my,mz
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1   1/2
)
 t (1/2,1/2,1/2) +1 { 1 | 1/2 1/2 1/2 }
18 -y+1/2, x+1/2, z+1/2, +1
-my,mx,mz
(
   0  -1   0   1/2
   1   0   0   1/2
   0   0   1   1/2
)
 4+ (0,0,1/2) 0,1/2,z +1 { 4+001 | 1/2 1/2 1/2 }
19 y+1/2, -x+1/2, z+1/2, +1
my,-mx,mz
(
   0   1   0   1/2
  -1   0   0   1/2
   0   0   1   1/2
)
 4- (0,0,1/2) 1/2,0,z +1 { 4-001 | 1/2 1/2 1/2 }
20 -x+1/2, -y+1/2, z+1/2, +1
-mx,-my,mz
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0   1   1/2
)
 2 (0,0,1/2) 1/4,1/4,z +1 { 2001 | 1/2 1/2 1/2 }
21 -x+1/2, -y+1/2, -z+1/2, +1
mx, my, mz
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1   1/2
)
 -1 1/4,1/4,1/4 +1 { -1 | 1/2 1/2 1/2 }
22 y+1/2, -x+1/2, -z+1/2, +1
-my, mx, mz
(
   0   1   0   1/2
  -1   0   0   1/2
   0   0  -1   1/2
)
 -4+ 1/2,0,z 1/2,0,1/4 +1 { -4+001 | 1/2 1/2 1/2 }
23 -y+1/2, x+1/2, -z+1/2, +1
my, -mx, mz
(
   0  -1   0   1/2
   1   0   0   1/2
   0   0  -1   1/2
)
 -4- 0,1/2,z 0,1/2,1/4 +1 { -4-001 | 1/2 1/2 1/2 }
24 x+1/2, y+1/2, -z+1/2, +1
-mx, -my, mz
(
   1   0   0   1/2
   0   1   0   1/2
   0   0  -1   1/2
)
 n (1/2,1/2,0) x,y,1/4 +1 { m001 | 1/2 1/2 1/2 }
25 x+1/2, -y+1/2, -z+1/2, -1
-mx, my, mz
(
   1   0   0   1/2
   0  -1   0   1/2
   0   0  -1   1/2
)'
 2 (1/2,0,0) x,1/4,1/4 -1 { 2'100 | 1/2 1/2 1/2 }
26 -x+1/2, y+1/2, -z+1/2, -1
mx, -my, mz
(
  -1   0   0   1/2
   0   1   0   1/2
   0   0  -1   1/2
)'
 2 (0,1/2,0) 1/4,y,1/4 -1 { 2'010 | 1/2 1/2 1/2 }
27 y+1/2, x+1/2, -z+1/2, -1
-my, -mx, mz
(
   0   1   0   1/2
   1   0   0   1/2
   0   0  -1   1/2
)'
 2 (1/2,1/2,0) x,x,1/4 -1 { 2'110 | 1/2 1/2 1/2 }
28 -y+1/2, -x+1/2, -z+1/2, -1
my, mx, mz
(
   0  -1   0   1/2
  -1   0   0   1/2
   0   0  -1   1/2
)'
 2 x,-x+1/2,1/4 -1 { 2'1-10 | 1/2 1/2 1/2 }
29 -x+1/2, y+1/2, z+1/2, -1
-mx,my,mz
(
  -1   0   0   1/2
   0   1   0   1/2
   0   0   1   1/2
)'
 n (0,1/2,1/2) 1/4,y,z -1 { m'100 | 1/2 1/2 1/2 }
30 x+1/2, -y+1/2, z+1/2, -1
mx,-my,mz
(
   1   0   0   1/2
   0  -1   0   1/2
   0   0   1   1/2
)'
 n (1/2,0,1/2) x,1/4,z -1 { m'010 | 1/2 1/2 1/2 }
31 -y+1/2, -x+1/2, z+1/2, -1
-my,-mx,mz
(
   0  -1   0   1/2
  -1   0   0   1/2
   0   0   1   1/2
)'
 c x+1/2,-x,z -1 { m'110 | 1/2 1/2 1/2 }
32 y+1/2, x+1/2, z+1/2, -1
my,mx,mz
(
   0   1   0   1/2
   1   0   0   1/2
   0   0   1   1/2
)'
 n (1/2,1/2,1/2) x,x,z -1 { m'1-10 | 1/2 1/2 1/2 }

Go to the list of the Wyckoff Positions of the Group I4/mm'm' (#139.537)
Go to the Systematic Absences for the Group I4/mm'm' (#139.537)

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