General Positions of Magnetic Space Groups

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General Positions of the Group Pn-3m' (#224.113)
For this space group, BNS and OG settings coincide.
Its label in the OG setting is given as: Pn-3m' (#224.4.1614)

Standard/Default Setting

(x,y,z) form

Matrix form

Geom. interp.

Seitz notation

x, y, z, +1
m_x,m_y,m_z

   1   0   0    0
   0   1   0    0
   0   0   1    0

1 +1

{ 1 | 0 }

x, -y+1/2, -z+1/2, +1
m_x,-m_y,-m_z

   1   0   0    0
   0  -1   0   1/2
   0   0  -1   1/2

2 x,1/4,1/4 +1

{ 2₁₀₀ | 0 1/2 1/2 }

-x+1/2, y, -z+1/2, +1
-m_x,m_y,-m_z

  -1   0   0   1/2
   0   1   0    0
   0   0  -1   1/2

2 1/4,y,1/4 +1

{ 2₀₁₀ | 1/2 0 1/2 }

-x+1/2, -y+1/2, z, +1
-m_x,-m_y,m_z

  -1   0   0   1/2
   0  -1   0   1/2
   0   0   1    0

2 1/4,1/4,z +1

{ 2₀₀₁ | 1/2 1/2 0 }

z, x, y, +1
m_z,m_x,m_y

   0   0   1    0
   1   0   0    0
   0   1   0    0

3⁺ x,x,x +1

{ 3⁺₁₁₁ | 0 }

y, z, x, +1
m_y,m_z,m_x

   0   1   0    0
   0   0   1    0
   1   0   0    0

3^- x,x,x +1

{ 3^-₁₁₁ | 0 }

-y+1/2, z, -x+1/2, +1
-m_y,m_z,-m_x

   0  -1   0   1/2
   0   0   1    0
  -1   0   0   1/2

3^- x+1/2,-x,-x +1

{ 3^-_1-1-1 | 1/2 0 1/2 }

-z+1/2, -x+1/2, y, +1
-m_z,-m_x,m_y

   0   0  -1   1/2
  -1   0   0   1/2
   0   1   0    0

3⁺ x+1/2,-x,-x +1

{ 3⁺_1-1-1 | 1/2 1/2 0 }

-y+1/2, -z+1/2, x, +1
-m_y,-m_z,m_x

   0  -1   0   1/2
   0   0  -1   1/2
   1   0   0    0

3^- -x,x+1/2,-x +1

{ 3^-_-11-1 | 1/2 1/2 0 }

z, -x+1/2, -y+1/2, +1
m_z,-m_x,-m_y

   0   0   1    0
  -1   0   0   1/2
   0  -1   0   1/2

3⁺ -x,x+1/2,-x +1

{ 3⁺_-11-1 | 0 1/2 1/2 }

y, -z+1/2, -x+1/2, +1
m_y,-m_z,-m_x

   0   1   0    0
   0   0  -1   1/2
  -1   0   0   1/2

3^- -x+1/2,-x+1/2,x +1

{ 3^-_-1-11 | 0 1/2 1/2 }

-z+1/2, x, -y+1/2, +1
-m_z,m_x,-m_y

   0   0  -1   1/2
   1   0   0    0
   0  -1   0   1/2

3⁺ -x+1/2,-x+1/2,x +1

{ 3⁺_-1-11 | 1/2 0 1/2 }

-x, -y, -z, +1
m_x,m_y,m_z

  -1   0   0    0
   0  -1   0    0
   0   0  -1    0

-1 0,0,0 +1

{ -1 | 0 }

-x, y+1/2, z+1/2, +1
m_x,-m_y,-m_z

  -1   0   0    0
   0   1   0   1/2
   0   0   1   1/2

n (0,1/2,1/2) 0,y,z +1

{ m₁₀₀ | 0 1/2 1/2 }

x+1/2, -y, z+1/2, +1
-m_x,m_y,-m_z

   1   0   0   1/2
   0  -1   0    0
   0   0   1   1/2

n (1/2,0,1/2) x,0,z +1

{ m₀₁₀ | 1/2 0 1/2 }

x+1/2, y+1/2, -z, +1
-m_x,-m_y,m_z

   1   0   0   1/2
   0   1   0   1/2
   0   0  -1    0

n (1/2,1/2,0) x,y,0 +1

{ m₀₀₁ | 1/2 1/2 0 }

-z, -x, -y, +1
m_z,m_x,m_y

   0   0  -1    0
  -1   0   0    0
   0  -1   0    0

-3⁺ x,x,x 0,0,0 +1

{ -3⁺₁₁₁ | 0 }

-y, -z, -x, +1
m_y,m_z,m_x

   0  -1   0    0
   0   0  -1    0
  -1   0   0    0

-3^- x,x,x 0,0,0 +1

{ -3^-₁₁₁ | 0 }

y+1/2, -z, x+1/2, +1
-m_y,m_z,-m_x

   0   1   0   1/2
   0   0  -1    0
   1   0   0   1/2

-3^- x+1/2,-x,-x 0,-1/2,1/2 +1

{ -3^-_1-1-1 | 1/2 0 1/2 }

z+1/2, x+1/2, -y, +1
-m_z,-m_x,m_y

   0   0   1   1/2
   1   0   0   1/2
   0  -1   0    0

-3⁺ x-0.5,-x+1,-x 0,1/2,-1/2 +1

{ -3⁺_1-1-1 | 1/2 1/2 0 }

y+1/2, z+1/2, -x, +1
-m_y,-m_z,m_x

   0   1   0   1/2
   0   0   1   1/2
  -1   0   0    0

-3^- -x+1,x-1/2,-x 1/2,0,-1/2 +1

{ -3^-_-11-1 | 1/2 1/2 0 }

-z, x+1/2, y+1/2, +1
m_z,-m_x,-m_y

   0   0  -1    0
   1   0   0   1/2
   0   1   0   1/2

-3⁺ -x-1,x+1/2,-x -1/2,0,1/2 +1

{ -3⁺_-11-1 | 0 1/2 1/2 }

-y, z+1/2, x+1/2, +1
m_y,-m_z,-m_x

   0  -1   0    0
   0   0   1   1/2
   1   0   0   1/2

-3^- -x-1/2,-x+1/2,x -1/2,1/2,0 +1

{ -3^-_-1-11 | 0 1/2 1/2 }

z+1/2, -x, y+1/2, +1
-m_z,m_x,-m_y

   0   0   1   1/2
  -1   0   0    0
   0   1   0   1/2

-3⁺ -x+1/2,-x,x 1/2,-1/2,0 +1

{ -3⁺_-1-11 | 1/2 0 1/2 }

x+1/2, -z, y+1/2, -1
-m_x,m_z,-m_y

   1   0   0   1/2
   0   0  -1    0
   0   1   0   1/2

4⁺ (1/2,0,0) x,-1/4,1/4 -1

{ 4'⁺₁₀₀ | 1/2 0 1/2 }

x+1/2, z+1/2, -y, -1
-m_x,-m_z,m_y

   1   0   0   1/2
   0   0   1   1/2
   0  -1   0    0

4^- (1/2,0,0) x,1/4,-1/4 -1

{ 4'^-₁₀₀ | 1/2 1/2 0 }

z+1/2, y+1/2, -x, -1
-m_z,-m_y,m_x

   0   0   1   1/2
   0   1   0   1/2
  -1   0   0    0

4⁺ (0,1/2,0) 1/4,y,-1/4 -1

{ 4'⁺₀₁₀ | 1/2 1/2 0 }

-z, y+1/2, x+1/2, -1
m_z,-m_y,-m_x

   0   0  -1    0
   0   1   0   1/2
   1   0   0   1/2

4^- (0,1/2,0) -1/4,y,1/4 -1

{ 4'^-₀₁₀ | 0 1/2 1/2 }

-y, x+1/2, z+1/2, -1
m_y,-m_x,-m_z

   0  -1   0    0
   1   0   0   1/2
   0   0   1   1/2

4⁺ (0,0,1/2) -1/4,1/4,z -1

{ 4'⁺₀₀₁ | 0 1/2 1/2 }

y+1/2, -x, z+1/2, -1
-m_y,m_x,-m_z

   0   1   0   1/2
  -1   0   0    0
   0   0   1   1/2

4^- (0,0,1/2) 1/4,-1/4,z -1

{ 4'^-₀₀₁ | 1/2 0 1/2 }

y+1/2, x+1/2, -z, -1
-m_y,-m_x,m_z

   0   1   0   1/2
   1   0   0   1/2
   0   0  -1    0

2 (1/2,1/2,0) x,x,0 -1

{ 2'₁₁₀ | 1/2 1/2 0 }

-y, -x, -z, -1
m_y,m_x,m_z

   0  -1   0    0
  -1   0   0    0
   0   0  -1    0

2 x,-x,0 -1

{ 2'_1-10 | 0 }

-x, z+1/2, y+1/2, -1
m_x,-m_z,-m_y

  -1   0   0    0
   0   0   1   1/2
   0   1   0   1/2

2 (0,1/2,1/2) 0,y,y -1

{ 2'₀₁₁ | 0 1/2 1/2 }

-x, -z, -y, -1
m_x,m_z,m_y

  -1   0   0    0
   0   0  -1    0
   0  -1   0    0

2 0,y,-y -1

{ 2'_01-1 | 0 }

z+1/2, -y, x+1/2, -1
-m_z,m_y,-m_x

   0   0   1   1/2
   0  -1   0    0
   1   0   0   1/2

2 (1/2,0,1/2) x,0,x -1

{ 2'₁₀₁ | 1/2 0 1/2 }

-z, -y, -x, -1
m_z,m_y,m_x

   0   0  -1    0
   0  -1   0    0
  -1   0   0    0

2 -x,0,x -1

{ 2'_-101 | 0 }

-x+1/2, z, -y+1/2, -1
-m_x,m_z,-m_y

  -1   0   0   1/2
   0   0   1    0
   0  -1   0   1/2

-4⁺ x,1/4,1/4 1/4,1/4,1/4 -1

{ -4'⁺₁₀₀ | 1/2 0 1/2 }

-x+1/2, -z+1/2, y, -1
-m_x,-m_z,m_y

  -1   0   0   1/2
   0   0  -1   1/2
   0   1   0    0

-4^- x,1/4,1/4 1/4,1/4,1/4 -1

{ -4'^-₁₀₀ | 1/2 1/2 0 }

-z+1/2, -y+1/2, x, -1
-m_z,-m_y,m_x

   0   0  -1   1/2
   0  -1   0   1/2
   1   0   0    0

-4⁺ 1/4,y,1/4 1/4,1/4,1/4 -1

{ -4'⁺₀₁₀ | 1/2 1/2 0 }

z, -y+1/2, -x+1/2, -1
m_z,-m_y,-m_x

   0   0   1    0
   0  -1   0   1/2
  -1   0   0   1/2

-4^- 1/4,y,1/4 1/4,1/4,1/4 -1

{ -4'^-₀₁₀ | 0 1/2 1/2 }

y, -x+1/2, -z+1/2, -1
m_y,-m_x,-m_z

   0   1   0    0
  -1   0   0   1/2
   0   0  -1   1/2

-4⁺ 1/4,1/4,z 1/4,1/4,1/4 -1

{ -4'⁺₀₀₁ | 0 1/2 1/2 }

-y+1/2, x, -z+1/2, -1
-m_y,m_x,-m_z

   0  -1   0   1/2
   1   0   0    0
   0   0  -1   1/2

-4^- 1/4,1/4,z 1/4,1/4,1/4 -1

{ -4'^-₀₀₁ | 1/2 0 1/2 }

-y+1/2, -x+1/2, z, -1
-m_y,-m_x,m_z

   0  -1   0   1/2
  -1   0   0   1/2
   0   0   1    0

m x+1/2,-x,z -1

{ m'₁₁₀ | 1/2 1/2 0 }

y, x, z, -1
m_y,m_x,m_z

   0   1   0    0
   1   0   0    0
   0   0   1    0

m x,x,z -1

{ m'_1-10 | 0 }

x, -z+1/2, -y+1/2, -1
m_x,-m_z,-m_y

   1   0   0    0
   0   0  -1   1/2
   0  -1   0   1/2

m x,y+1/2,-y -1

{ m'₀₁₁ | 0 1/2 1/2 }

x, z, y, -1
m_x,m_z,m_y

   1   0   0    0
   0   0   1    0
   0   1   0    0

m x,y,y -1

{ m'_01-1 | 0 }

-z+1/2, y, -x+1/2, -1
-m_z,m_y,-m_x

   0   0  -1   1/2
   0   1   0    0
  -1   0   0   1/2

m -x+1/2,y,x -1

{ m'₁₀₁ | 1/2 0 1/2 }

z, y, x, -1
m_z,m_y,m_x

   0   0   1    0
   0   1   0    0
   1   0   0    0

m x,y,x -1

{ m'_-101 | 0 }

Go to the list of the Wyckoff Positions of the Group Pn-3m' (#224.113)
Go to the Systematic Absences for the Group Pn-3m' (#224.113)

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General Positions of the Group Pn-3m' (#224.113) For this space group, BNS and OG settings coincide.Its label in the OG setting is given as: Pn-3m' (#224.4.1614)

General Positions of the Group Pn-3m' (#224.113)
For this space group, BNS and OG settings coincide.
Its label in the OG setting is given as: Pn-3m' (#224.4.1614)