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General Positions of the Group I41/a'cd (#142.563)
For this space group, BNS and OG settings coincide.
Its label in the OG setting is given as: I41/a'cd (#142.3.1224)

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+1/4, x+3/4, z+1/4, +1
-my,mx,mz
(
   0  -1   0   1/4
   1   0   0   3/4
   0   0   1   1/4
)
 4+ (0,0,1/4) -1/4,1/2,z +1 { 4+001 | 1/4 3/4 1/4 }
3 y+3/4, -x+3/4, z+1/4, +1
my,-mx,mz
(
   0   1   0   3/4
  -1   0   0   3/4
   0   0   1   1/4
)
 4- (0,0,1/4) 3/4,0,z +1 { 4-001 | 3/4 3/4 1/4 }
4 -x, -y+1/2, z, +1
-mx,-my,mz
(
  -1   0   0    0
   0  -1   0   1/2
   0   0   1    0
)
 2 0,1/4,z +1 { 2001 | 0 1/2 0 }
5 -x, y, z+1/2, +1
mx,-my,-mz
(
  -1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
 c 0,y,z +1 { m100 | 0 0 1/2 }
6 x, -y+1/2, z+1/2, +1
-mx,my,-mz
(
   1   0   0    0
   0  -1   0   1/2
   0   0   1   1/2
)
 c x,1/4,z +1 { m010 | 0 1/2 1/2 }
7 -y+3/4, -x+1/4, z+1/4, +1
my,mx,-mz
(
   0  -1   0   3/4
  -1   0   0   1/4
   0   0   1   1/4
)
 d (1/4,-1/4,1/4) x+1/2,-x,z +1 { m110 | 3/4 1/4 1/4 }
8 y+1/4, x+1/4, z+1/4, +1
-my,-mx,-mz
(
   0   1   0   1/4
   1   0   0   1/4
   0   0   1   1/4
)
 d (1/4,1/4,1/4) x,x,z +1 { m1-10 | 1/4 1/4 1/4 }
9 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 { 2'100 | 1/2 1/2 0 }
10 -x+1/2, y, -z, -1
mx,-my,mz
(
  -1   0   0   1/2
   0   1   0    0
   0   0  -1    0
)'
 2 1/4,y,0 -1 { 2'010 | 1/2 0 0 }
11 y+3/4, x+1/4, -z+1/4, -1
-my,-mx,mz
(
   0   1   0   3/4
   1   0   0   1/4
   0   0  -1   1/4
)'
 2 (1/2,1/2,0) x,x-1/4,1/8 -1 { 2'110 | 3/4 1/4 1/4 }
12 -y+1/4, -x+1/4, -z+1/4, -1
my,mx,mz
(
   0  -1   0   1/4
  -1   0   0   1/4
   0   0  -1   1/4
)'
 2 x,-x+1/4,1/8 -1 { 2'1-10 | 1/4 1/4 1/4 }
13 -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 }
14 y+3/4, -x+1/4, -z+3/4, -1
my,-mx,-mz
(
   0   1   0   3/4
  -1   0   0   1/4
   0   0  -1   3/4
)'
 -4+ 1/2,-1/4,z 1/2,-1/4,3/8 -1 { -4'+001 | 3/4 1/4 3/4 }
15 -y+1/4, x+1/4, -z+3/4, -1
-my,mx,-mz
(
   0  -1   0   1/4
   1   0   0   1/4
   0   0  -1   3/4
)'
 -4- 0,1/4,z 0,1/4,3/8 -1 { -4'-001 | 1/4 1/4 3/4 }
16 x, y+1/2, -z, -1
mx,my,-mz
(
   1   0   0    0
   0   1   0   1/2
   0   0  -1    0
)'
 b x,y,0 -1 { m'001 | 0 1/2 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+3/4, x+1/4, z+3/4, +1
-my,mx,mz
(
   0  -1   0   3/4
   1   0   0   1/4
   0   0   1   3/4
)
 4+ (0,0,3/4) 1/4,1/2,z +1 { 4+001 | 3/4 1/4 3/4 }
19 y+1/4, -x+1/4, z+3/4, +1
my,-mx,mz
(
   0   1   0   1/4
  -1   0   0   1/4
   0   0   1   3/4
)
 4- (0,0,3/4) 1/4,0,z +1 { 4-001 | 1/4 1/4 3/4 }
20 -x+1/2, -y, z+1/2, +1
-mx,-my,mz
(
  -1   0   0   1/2
   0  -1   0    0
   0   0   1   1/2
)
 2 (0,0,1/2) 1/4,0,z +1 { 2001 | 1/2 0 1/2 }
21 -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 }
22 x+1/2, -y, z, +1
-mx, my, -mz
(
   1   0   0   1/2
   0  -1   0    0
   0   0   1    0
)
 a x,0,z +1 { m010 | 1/2 0 0 }
23 -y+1/4, -x+3/4, z+3/4, +1
my, mx, -mz
(
   0  -1   0   1/4
  -1   0   0   3/4
   0   0   1   3/4
)
 d (-1/4,1/4,3/4) x+1/2,-x,z +1 { m110 | 1/4 3/4 3/4 }
24 y+3/4, x+3/4, z+3/4, +1
-my, -mx, -mz
(
   0   1   0   3/4
   1   0   0   3/4
   0   0   1   3/4
)
 d (3/4,3/4,3/4) x,x,z +1 { m1-10 | 3/4 3/4 3/4 }
25 x, -y, -z+1/2, -1
-mx, my, mz
(
   1   0   0    0
   0  -1   0    0
   0   0  -1   1/2
)'
 2 x,0,1/4 -1 { 2'100 | 0 0 1/2 }
26 -x, y+1/2, -z+1/2, -1
mx, -my, mz
(
  -1   0   0    0
   0   1   0   1/2
   0   0  -1   1/2
)'
 2 (0,1/2,0) 0,y,1/4 -1 { 2'010 | 0 1/2 1/2 }
27 y+1/4, x+3/4, -z+3/4, -1
-my, -mx, mz
(
   0   1   0   1/4
   1   0   0   3/4
   0   0  -1   3/4
)'
 2 (1/2,1/2,0) x,x+1/4,3/8 -1 { 2'110 | 1/4 3/4 3/4 }
28 -y+3/4, -x+3/4, -z+3/4, -1
my, mx, mz
(
   0  -1   0   3/4
  -1   0   0   3/4
   0   0  -1   3/4
)'
 2 x,-x+3/4,3/8 -1 { 2'1-10 | 3/4 3/4 3/4 }
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
)'
 -1 1/4,1/4,1/4 -1 { -1' | 1/2 1/2 1/2 }
30 y+1/4, -x+3/4, -z+1/4, -1
my,-mx,-mz
(
   0   1   0   1/4
  -1   0   0   3/4
   0   0  -1   1/4
)'
 -4+ 1/2,1/4,z 1/2,1/4,1/8 -1 { -4'+001 | 1/4 3/4 1/4 }
31 -y+3/4, x+3/4, -z+1/4, -1
-my,mx,-mz
(
   0  -1   0   3/4
   1   0   0   3/4
   0   0  -1   1/4
)'
 -4- 0,3/4,z 0,3/4,1/8 -1 { -4'-001 | 3/4 3/4 1/4 }
32 x+1/2, y, -z+1/2, -1
mx,my,-mz
(
   1   0   0   1/2
   0   1   0    0
   0   0  -1   1/2
)'
 a x,y,1/4 -1 { m'001 | 1/2 0 1/2 }

Go to the list of the Wyckoff Positions of the Group I41/a'cd (#142.563)
Go to the Systematic Absences for the Group I41/a'cd (#142.563)

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