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I4/m'm'm' [#139.539] (Type: 3 -- Type III (translationgleiche))

[OG: I4/m'm'm' #139.9.1187]

Wyckoff Positions of Group 139.539 (I4/m'm'm')

Multiplicity Wyckoff
letter
Coordinates
(0,0,0) +(1/2,1/2,1/2) + 
32o
(x,y,z | mx,my,mz) (-y,x,z | -my,mx,mz) (y,-x,z | my,-mx,mz)
(x,-y,-z | mx,-my,-mz) (-x,y,-z | -mx,my,-mz) (-x,-y,z | -mx,-my,mz)
(y,x,-z | my,mx,-mz) (-y,-x,-z | -my,-mx,-mz) (-x,-y,-z | -mx,-my,-mz)
(y,-x,-z | my,-mx,-mz) (-y,x,-z | -my,mx,-mz) (-x,y,z | -mx,my,mz)
(x,-y,z | mx,-my,mz) (x,y,-z | mx,my,-mz) (-y,-x,z | -my,-mx,mz)
(y,x,z | my,mx,mz)
16n
(0,y,z | 0,my,mz) (-y,0,z | -my,0,mz) (y,0,z | my,0,mz)
(0,-y,-z | 0,-my,-mz) (0,y,-z | 0,my,-mz) (0,-y,z | 0,-my,mz)
(y,0,-z | my,0,-mz) (-y,0,-z | -my,0,-mz)
16m
(x,x,z | mx,mx,mz) (-x,x,z | -mx,mx,mz) (x,-x,z | mx,-mx,mz)
(x,-x,-z | mx,-mx,-mz) (-x,x,-z | -mx,mx,-mz) (-x,-x,z | -mx,-mx,mz)
(x,x,-z | mx,mx,-mz) (-x,-x,-z | -mx,-mx,-mz)
16l
(x,y,0 | mx,my,0) (-y,x,0 | -my,mx,0) (y,-x,0 | my,-mx,0)
(x,-y,0 | mx,-my,0) (-x,y,0 | -mx,my,0) (-x,-y,0 | -mx,-my,0)
(y,x,0 | my,mx,0) (-y,-x,0 | -my,-mx,0)
16k
(x,x+1/2,1/4 | mx,mx,0) (-x,x+1/2,3/4 | -mx,mx,0) (x,-x+1/2,3/4 | mx,-mx,0)
(-x,-x+1/2,1/4 | -mx,-mx,0) (-x,-x+1/2,3/4 | -mx,-mx,0) (x,-x+1/2,1/4 | mx,-mx,0)
(-x,x+1/2,1/4 | -mx,mx,0) (x,x+1/2,3/4 | mx,mx,0)
8j
(x,1/2,0 | mx,0,0) (1/2,x,0 | 0,mx,0) (1/2,-x,0 | 0,-mx,0)
(-x,1/2,0 | -mx,0,0)
8i
(x,0,0 | mx,0,0) (0,x,0 | 0,mx,0) (0,-x,0 | 0,-mx,0)
(-x,0,0 | -mx,0,0)
8h
(x,x,0 | mx,mx,0) (-x,x,0 | -mx,mx,0) (x,-x,0 | mx,-mx,0)
(-x,-x,0 | -mx,-mx,0)
8g
(0,1/2,z | 0,0,mz) (1/2,0,z | 0,0,mz) (0,1/2,-z | 0,0,-mz)
(1/2,0,-z | 0,0,-mz)
8f
(1/4,1/4,1/4 | 0,0,0) (1/4,3/4,3/4 | 0,0,0) (3/4,1/4,3/4 | 0,0,0)
(3/4,3/4,1/4 | 0,0,0)
4e
(0,0,z | 0,0,mz) (0,0,-z | 0,0,-mz)
4d
(0,1/2,1/4 | 0,0,0) (0,1/2,3/4 | 0,0,0)
4c
(0,1/2,0 | 0,0,0) (1/2,0,0 | 0,0,0)
2b
(0,0,1/2 | 0,0,0)
2a
(0,0,0 | 0,0,0)

Site Symmetries of the Wyckoff Positions

WPRepresentativePG
2a(0,0,0 | 0,0,0)4/m'm'm'
2b(0,0,1/2 | 0,0,0)4/m'm'm'
4c(0,1/2,0 | 0,0,0)m'm'm'
4d(0,1/2,1/4 | 0,0,0)-4'2m'
4e(0,0,z | 0,0,mz)4
8f(1/4,1/4,1/4 | 0,0,0)2/m'
8g(0,1/2,z | 0,0,mz)2
8h(x,x,0 | mx,mx,0)2
8i(x,0,0 | mx,0,0)2
8j(x,1/2,0 | mx,0,0)2
16k(x,x+1/2,1/4 | mx,mx,0)2
16l(x,y,0 | mx,my,0)1
16m(x,x,z | mx,mx,mz)1
16n(0,y,z | 0,my,mz)1
32o(x,y,z | mx,my,mz)1

List all the elements of the orbits


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Go to the extinction rules of (I4/m'm'm')



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