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General Positions of the Group P41'32' (#213.65)
For this space group, BNS and OG settings coincide.
Its label in the OG setting is given as: P41'32' (#213.3.1566)

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 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 }
3 -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 { 2010 | 0 1/2 1/2 }
4 -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 }
5 z, x, y, +1
mz,mx,my
(
   0   0   1    0
   1   0   0    0
   0   1   0    0
)
 3+ x,x,x +1 { 3+111 | 0 }
6 y, z, x, +1
my,mz,mx
(
   0   1   0    0
   0   0   1    0
   1   0   0    0
)
 3- x,x,x +1 { 3-111 | 0 }
7 -y, z+1/2, -x+1/2, +1
-my,mz,-mx
(
   0  -1   0    0
   0   0   1   1/2
  -1   0   0   1/2
)
 3- (-1/3,1/3,1/3) x+1/6,-x+1/6,-x +1 { 3-1-1-1 | 0 1/2 1/2 }
8 -z+1/2, -x, y+1/2, +1
-mz,-mx,my
(
   0   0  -1   1/2
  -1   0   0    0
   0   1   0   1/2
)
 3+ x+1/2,-x,-x +1 { 3+1-1-1 | 1/2 0 1/2 }
9 -y+1/2, -z, x+1/2, +1
-my,-mz,mx
(
   0  -1   0   1/2
   0   0  -1    0
   1   0   0   1/2
)
 3- (1/3,-1/3,1/3) -x-1/6,x+1/3,-x +1 { 3--11-1 | 1/2 0 1/2 }
10 z+1/2, -x+1/2, -y, +1
mz,-mx,-my
(
   0   0   1   1/2
  -1   0   0   1/2
   0  -1   0    0
)
 3+ -x+1/2,x,-x +1 { 3+-11-1 | 1/2 1/2 0 }
11 y+1/2, -z+1/2, -x, +1
my,-mz,-mx
(
   0   1   0   1/2
   0   0  -1   1/2
  -1   0   0    0
)
 3- (1/3,1/3,-1/3) -x+1/3,-x+1/6,x +1 { 3--1-11 | 1/2 1/2 0 }
12 -z, x+1/2, -y+1/2, +1
-mz,mx,-my
(
   0   0  -1    0
   1   0   0   1/2
   0  -1   0   1/2
)
 3+ -x,-x+1/2,x +1 { 3+-1-11 | 0 1/2 1/2 }
13 x+1/4, -z+1/4, y+3/4, -1
-mx,mz,-my
(
   1   0   0   1/4
   0   0  -1   1/4
   0   1   0   3/4
)'
 4+ (1/4,0,0) x,-1/4,1/2 -1 { 4'+100 | 1/4 1/4 3/4 }
14 x+3/4, z+1/4, -y+1/4, -1
-mx,-mz,my
(
   1   0   0   3/4
   0   0   1   1/4
   0  -1   0   1/4
)'
 4- (3/4,0,0) x,1/4,0 -1 { 4'-100 | 3/4 1/4 1/4 }
15 z+3/4, y+1/4, -x+1/4, -1
-mz,-my,mx
(
   0   0   1   3/4
   0   1   0   1/4
  -1   0   0   1/4
)'
 4+ (0,1/4,0) 1/2,y,-1/4 -1 { 4'+010 | 3/4 1/4 1/4 }
16 -z+1/4, y+3/4, x+1/4, -1
mz,-my,-mx
(
   0   0  -1   1/4
   0   1   0   3/4
   1   0   0   1/4
)'
 4- (0,3/4,0) 0,y,1/4 -1 { 4'-010 | 1/4 3/4 1/4 }
17 -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 }
18 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 }
19 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 }
20 -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 }
21 -x+1/4, z+3/4, y+1/4, -1
mx,-mz,-my
(
  -1   0   0   1/4
   0   0   1   3/4
   0   1   0   1/4
)'
 2 (0,1/2,1/2) 1/8,y+1/4,y -1 { 2'011 | 1/4 3/4 1/4 }
22 -x+3/4, -z+3/4, -y+3/4, -1
mx,mz,my
(
  -1   0   0   3/4
   0   0  -1   3/4
   0  -1   0   3/4
)'
 2 3/8,y+3/4,-y -1 { 2'01-1 | 3/4 3/4 3/4 }
23 z+1/4, -y+1/4, x+3/4, -1
-mz,my,-mx
(
   0   0   1   1/4
   0  -1   0   1/4
   1   0   0   3/4
)'
 2 (1/2,0,1/2) x-0.25,1/8,x -1 { 2'101 | 1/4 1/4 3/4 }
24 -z+3/4, -y+3/4, -x+3/4, -1
mz,my,mx
(
   0   0  -1   3/4
   0  -1   0   3/4
  -1   0   0   3/4
)'
 2 -x+3/4,3/8,x -1 { 2'-101 | 3/4 3/4 3/4 }

Go to the list of the Wyckoff Positions of the Group P41'32' (#213.65)
Go to the Systematic Absences for the Group P41'32' (#213.65)

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