General Positions of Magnetic Space Groups

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General Positions of the Group Fd-3m' (#227.131)
**227.131 Fd-3m' (UNI symbol)**

For this space group, BNS and OG settings coincide.
Its label in the OG setting is given as: Fd-3m' (#227.4.1631)

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+1/4, -z+1/4, +1
m_x,-m_y,-m_z

   1   0   0    0
   0  -1   0   1/4
   0   0  -1   1/4

2 x,1/8,1/8 +1

{ 2₁₀₀ | 0 1/4 1/4 }

-x+1/4, y, -z+1/4, +1
-m_x,m_y,-m_z

  -1   0   0   1/4
   0   1   0    0
   0   0  -1   1/4

2 1/8,y,1/8 +1

{ 2₀₁₀ | 1/4 0 1/4 }

-x+1/4, -y+1/4, z, +1
-m_x,-m_y,m_z

  -1   0   0   1/4
   0  -1   0   1/4
   0   0   1    0

2 1/8,1/8,z +1

{ 2₀₀₁ | 1/4 1/4 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+1/4, z, -x+1/4, +1
-m_y,m_z,-m_x

   0  -1   0   1/4
   0   0   1    0
  -1   0   0   1/4

3^- x+1/4,-x,-x +1

{ 3^-_1-1-1 | 1/4 0 1/4 }

-z+1/4, -x+1/4, y, +1
-m_z,-m_x,m_y

   0   0  -1   1/4
  -1   0   0   1/4
   0   1   0    0

3⁺ x+1/4,-x,-x +1

{ 3⁺_1-1-1 | 1/4 1/4 0 }

-y+1/4, -z+1/4, x, +1
-m_y,-m_z,m_x

   0  -1   0   1/4
   0   0  -1   1/4
   1   0   0    0

3^- -x,x+1/4,-x +1

{ 3^-_-11-1 | 1/4 1/4 0 }

z, -x+1/4, -y+1/4, +1
m_z,-m_x,-m_y

   0   0   1    0
  -1   0   0   1/4
   0  -1   0   1/4

3⁺ -x,x+1/4,-x +1

{ 3⁺_-11-1 | 0 1/4 1/4 }

y, -z+1/4, -x+1/4, +1
m_y,-m_z,-m_x

   0   1   0    0
   0   0  -1   1/4
  -1   0   0   1/4

3^- -x+1/4,-x+1/4,x +1

{ 3^-_-1-11 | 0 1/4 1/4 }

-z+1/4, x, -y+1/4, +1
-m_z,m_x,-m_y

   0   0  -1   1/4
   1   0   0    0
   0  -1   0   1/4

3⁺ -x+1/4,-x+1/4,x +1

{ 3⁺_-1-11 | 1/4 0 1/4 }

-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+1/4, z+1/4, +1
m_x,-m_y,-m_z

  -1   0   0    0
   0   1   0   1/4
   0   0   1   1/4

d (0,1/4,1/4) 0,y,z +1

{ m₁₀₀ | 0 1/4 1/4 }

x+1/4, -y, z+1/4, +1
-m_x,m_y,-m_z

   1   0   0   1/4
   0  -1   0    0
   0   0   1   1/4

d (1/4,0,1/4) x,0,z +1

{ m₀₁₀ | 1/4 0 1/4 }

x+1/4, y+1/4, -z, +1
-m_x,-m_y,m_z

   1   0   0   1/4
   0   1   0   1/4
   0   0  -1    0

d (1/4,1/4,0) x,y,0 +1

{ m₀₀₁ | 1/4 1/4 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+1/4, -z, x+1/4, +1
-m_y,m_z,-m_x

   0   1   0   1/4
   0   0  -1    0
   1   0   0   1/4

-3^- x+1/4,-x,-x 0,-1/4,1/4 +1

{ -3^-_1-1-1 | 1/4 0 1/4 }

z+1/4, x+1/4, -y, +1
-m_z,-m_x,m_y

   0   0   1   1/4
   1   0   0   1/4
   0  -1   0    0

-3⁺ x-0.25,-x+1/2,-x 0,1/4,-1/4 +1

{ -3⁺_1-1-1 | 1/4 1/4 0 }

y+1/4, z+1/4, -x, +1
-m_y,-m_z,m_x

   0   1   0   1/4
   0   0   1   1/4
  -1   0   0    0

-3^- -x+1/2,x-1/4,-x 1/4,0,-1/4 +1

{ -3^-_-11-1 | 1/4 1/4 0 }

-z, x+1/4, y+1/4, +1
m_z,-m_x,-m_y

   0   0  -1    0
   1   0   0   1/4
   0   1   0   1/4

-3⁺ -x-1/2,x+1/4,-x -1/4,0,1/4 +1

{ -3⁺_-11-1 | 0 1/4 1/4 }

-y, z+1/4, x+1/4, +1
m_y,-m_z,-m_x

   0  -1   0    0
   0   0   1   1/4
   1   0   0   1/4

-3^- -x-1/4,-x+1/4,x -1/4,1/4,0 +1

{ -3^-_-1-11 | 0 1/4 1/4 }

z+1/4, -x, y+1/4, +1
-m_z,m_x,-m_y

   0   0   1   1/4
  -1   0   0    0
   0   1   0   1/4

-3⁺ -x+1/4,-x,x 1/4,-1/4,0 +1

{ -3⁺_-1-11 | 1/4 0 1/4 }

x+1/4, -z, y+1/4, -1
-m_x,m_z,-m_y

   1   0   0   1/4
   0   0  -1    0
   0   1   0   1/4

4⁺ (1/4,0,0) x,-1/8,1/8 -1

{ 4'⁺₁₀₀ | 1/4 0 1/4 }

x+1/4, z+1/4, -y, -1
-m_x,-m_z,m_y

   1   0   0   1/4
   0   0   1   1/4
   0  -1   0    0

4^- (1/4,0,0) x,1/8,-1/8 -1

{ 4'^-₁₀₀ | 1/4 1/4 0 }

z+1/4, y+1/4, -x, -1
-m_z,-m_y,m_x

   0   0   1   1/4
   0   1   0   1/4
  -1   0   0    0

4⁺ (0,1/4,0) 1/8,y,-1/8 -1

{ 4'⁺₀₁₀ | 1/4 1/4 0 }

-z, y+1/4, x+1/4, -1
m_z,-m_y,-m_x

   0   0  -1    0
   0   1   0   1/4
   1   0   0   1/4

4^- (0,1/4,0) -1/8,y,1/8 -1

{ 4'^-₀₁₀ | 0 1/4 1/4 }

-y, x+1/4, z+1/4, -1
m_y,-m_x,-m_z

   0  -1   0    0
   1   0   0   1/4
   0   0   1   1/4

4⁺ (0,0,1/4) -1/8,1/8,z -1

{ 4'⁺₀₀₁ | 0 1/4 1/4 }

y+1/4, -x, z+1/4, -1
-m_y,m_x,-m_z

   0   1   0   1/4
  -1   0   0    0
   0   0   1   1/4

4^- (0,0,1/4) 1/8,-1/8,z -1

{ 4'^-₀₀₁ | 1/4 0 1/4 }

y+1/4, x+1/4, -z, -1
-m_y,-m_x,m_z

   0   1   0   1/4
   1   0   0   1/4
   0   0  -1    0

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

{ 2'₁₁₀ | 1/4 1/4 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+1/4, y+1/4, -1
m_x,-m_z,-m_y

  -1   0   0    0
   0   0   1   1/4
   0   1   0   1/4

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

{ 2'₀₁₁ | 0 1/4 1/4 }

-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+1/4, -y, x+1/4, -1
-m_z,m_y,-m_x

   0   0   1   1/4
   0  -1   0    0
   1   0   0   1/4

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

{ 2'₁₀₁ | 1/4 0 1/4 }

-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+1/4, z, -y+1/4, -1
-m_x,m_z,-m_y

  -1   0   0   1/4
   0   0   1    0
   0  -1   0   1/4

-4⁺ x,1/8,1/8 1/8,1/8,1/8 -1

{ -4'⁺₁₀₀ | 1/4 0 1/4 }

-x+1/4, -z+1/4, y, -1
-m_x,-m_z,m_y

  -1   0   0   1/4
   0   0  -1   1/4
   0   1   0    0

-4^- x,1/8,1/8 1/8,1/8,1/8 -1

{ -4'^-₁₀₀ | 1/4 1/4 0 }

-z+1/4, -y+1/4, x, -1
-m_z,-m_y,m_x

   0   0  -1   1/4
   0  -1   0   1/4
   1   0   0    0

-4⁺ 1/8,y,1/8 1/8,1/8,1/8 -1

{ -4'⁺₀₁₀ | 1/4 1/4 0 }

z, -y+1/4, -x+1/4, -1
m_z,-m_y,-m_x

   0   0   1    0
   0  -1   0   1/4
  -1   0   0   1/4

-4^- 1/8,y,1/8 1/8,1/8,1/8 -1

{ -4'^-₀₁₀ | 0 1/4 1/4 }

y, -x+1/4, -z+1/4, -1
m_y,-m_x,-m_z

   0   1   0    0
  -1   0   0   1/4
   0   0  -1   1/4

-4⁺ 1/8,1/8,z 1/8,1/8,1/8 -1

{ -4'⁺₀₀₁ | 0 1/4 1/4 }

-y+1/4, x, -z+1/4, -1
-m_y,m_x,-m_z

   0  -1   0   1/4
   1   0   0    0
   0   0  -1   1/4

-4^- 1/8,1/8,z 1/8,1/8,1/8 -1

{ -4'^-₀₀₁ | 1/4 0 1/4 }

-y+1/4, -x+1/4, z, -1
-m_y,-m_x,m_z

   0  -1   0   1/4
  -1   0   0   1/4
   0   0   1    0

m x+1/4,-x,z -1

{ m'₁₁₀ | 1/4 1/4 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+1/4, -y+1/4, -1
m_x,-m_z,-m_y

   1   0   0    0
   0   0  -1   1/4
   0  -1   0   1/4

m x,y+1/4,-y -1

{ m'₀₁₁ | 0 1/4 1/4 }

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+1/4, y, -x+1/4, -1
-m_z,m_y,-m_x

   0   0  -1   1/4
   0   1   0    0
  -1   0   0   1/4

m -x+1/4,y,x -1

{ m'₁₀₁ | 1/4 0 1/4 }

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 }

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

t (0,1/2,1/2) +1

{ 1 | 0 1/2 1/2 }

x, -y+3/4, -z+3/4, +1
m_x,-m_y,-m_z

   1   0   0    0
   0  -1   0   3/4
   0   0  -1   3/4

2 x,3/8,3/8 +1

{ 2₁₀₀ | 0 3/4 3/4 }

-x+1/4, y+1/2, -z+3/4, +1
-m_x,m_y,-m_z

  -1   0   0   1/4
   0   1   0   1/2
   0   0  -1   3/4

2 (0,1/2,0) 1/8,y,3/8 +1

{ 2₀₁₀ | 1/4 1/2 3/4 }

-x+1/4, -y+3/4, z+1/2, +1
-m_x,-m_y,m_z

  -1   0   0   1/4
   0  -1   0   3/4
   0   0   1   1/2

2 (0,0,1/2) 1/8,3/8,z +1

{ 2₀₀₁ | 1/4 3/4 1/2 }

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⁺ (1/3,1/3,1/3) x-0.33333,x-1/6,x +1

{ 3⁺₁₁₁ | 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^- (1/3,1/3,1/3) x-0.16666,x+1/6,x +1

{ 3^-₁₁₁ | 0 1/2 1/2 }

-y+1/4, z+1/2, -x+3/4, +1
-m_y,m_z,-m_x

   0  -1   0   1/4
   0   0   1   1/2
  -1   0   0   3/4

3^- (-1/3,1/3,1/3) x+5/12,-x+1/6,-x +1

{ 3^-_1-1-1 | 1/4 1/2 3/4 }

-z+1/4, -x+3/4, y+1/2, +1
-m_z,-m_x,m_y

   0   0  -1   1/4
  -1   0   0   3/4
   0   1   0   1/2

3⁺ (-1/3,1/3,1/3) x+7/12,-x,-x +1

{ 3⁺_1-1-1 | 1/4 3/4 1/2 }

-y+1/4, -z+3/4, x+1/2, +1
-m_y,-m_z,m_x

   0  -1   0   1/4
   0   0  -1   3/4
   1   0   0   1/2

3^- -x-1/2,x+3/4,-x +1

{ 3^-_-11-1 | 1/4 3/4 1/2 }

z, -x+3/4, -y+3/4, +1
m_z,-m_x,-m_y

   0   0   1    0
  -1   0   0   3/4
   0  -1   0   3/4

3⁺ -x,x+3/4,-x +1

{ 3⁺_-11-1 | 0 3/4 3/4 }

y, -z+3/4, -x+3/4, +1
m_y,-m_z,-m_x

   0   1   0    0
   0   0  -1   3/4
  -1   0   0   3/4

3^- -x+3/4,-x+3/4,x +1

{ 3^-_-1-11 | 0 3/4 3/4 }

-z+1/4, x+1/2, -y+3/4, +1
-m_z,m_x,-m_y

   0   0  -1   1/4
   1   0   0   1/2
   0  -1   0   3/4

3⁺ -x+1/4,-x+3/4,x +1

{ 3⁺_-1-11 | 1/4 1/2 3/4 }

-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

-1 0,1/4,1/4 +1

{ -1 | 0 1/2 1/2 }

-x, y+3/4, z+3/4, +1
m_x, -m_y, -m_z

  -1   0   0    0
   0   1   0   3/4
   0   0   1   3/4

d (0,3/4,3/4) 0,y,z +1

{ m₁₀₀ | 0 3/4 3/4 }

x+1/4, -y+1/2, z+3/4, +1
-m_x, m_y, -m_z

   1   0   0   1/4
   0  -1   0   1/2
   0   0   1   3/4

d (1/4,0,3/4) x,1/4,z +1

{ m₀₁₀ | 1/4 1/2 3/4 }

x+1/4, y+3/4, -z+1/2, +1
-m_x, -m_y, m_z

   1   0   0   1/4
   0   1   0   3/4
   0   0  -1   1/2

d (1/4,3/4,0) x,y,1/4 +1

{ m₀₀₁ | 1/4 3/4 1/2 }

-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 0,1/2,0 +1

{ -3⁺₁₁₁ | 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-0.5,x-1/2,x 0,0,1/2 +1

{ -3^-₁₁₁ | 0 1/2 1/2 }

y+1/4, -z+1/2, x+3/4, +1
-m_y, m_z, -m_x

   0   1   0   1/4
   0   0  -1   1/2
   1   0   0   3/4

-3^- x+3/4,-x,-x 0,-1/4,3/4 +1

{ -3^-_1-1-1 | 1/4 1/2 3/4 }

z+1/4, x+3/4, -y+1/2, +1
-m_z, -m_x, m_y

   0   0   1   1/4
   1   0   0   3/4
   0  -1   0   1/2

-3⁺ x-0.25,-x+1,-x 0,3/4,-1/4 +1

{ -3⁺_1-1-1 | 1/4 3/4 1/2 }

y+1/4, z+3/4, -x+1/2, +1
-m_y, -m_z, m_x

   0   1   0   1/4
   0   0   1   3/4
  -1   0   0   1/2

-3^- -x+1,x+1/4,-x 3/4,1/2,-1/4 +1

{ -3^-_-11-1 | 1/4 3/4 1/2 }

-z, x+3/4, y+3/4, +1
m_z, -m_x, -m_y

   0   0  -1    0
   1   0   0   3/4
   0   1   0   3/4

-3⁺ -x-3/2,x+3/4,-x -3/4,0,3/4 +1

{ -3⁺_-11-1 | 0 3/4 3/4 }

-y, z+3/4, x+3/4, +1
m_y, -m_z, -m_x

   0  -1   0    0
   0   0   1   3/4
   1   0   0   3/4

-3^- -x-3/4,-x+3/4,x -3/4,3/4,0 +1

{ -3^-_-1-11 | 0 3/4 3/4 }

z+1/4, -x+1/2, y+3/4, +1
-m_z, m_x, -m_y

   0   0   1   1/4
  -1   0   0   1/2
   0   1   0   3/4

-3⁺ -x+5/4,-x+1/4,x 3/4,-1/4,1/2 +1

{ -3⁺_-1-11 | 1/4 1/2 3/4 }

x+1/4, -z+1/2, y+3/4, -1
-m_x, m_z, -m_y

   1   0   0   1/4
   0   0  -1   1/2
   0   1   0   3/4

4⁺ (1/4,0,0) x,-1/8,5/8 -1

{ 4'⁺₁₀₀ | 1/4 1/2 3/4 }

x+1/4, z+3/4, -y+1/2, -1
-m_x, -m_z, m_y

   1   0   0   1/4
   0   0   1   3/4
   0  -1   0   1/2

4^- (1/4,0,0) x,5/8,-1/8 -1

{ 4'^-₁₀₀ | 1/4 3/4 1/2 }

z+1/4, y+3/4, -x+1/2, -1
-m_z, -m_y, m_x

   0   0   1   1/4
   0   1   0   3/4
  -1   0   0   1/2

4⁺ (0,3/4,0) 3/8,y,1/8 -1

{ 4'⁺₀₁₀ | 1/4 3/4 1/2 }

-z, y+3/4, x+3/4, -1
m_z, -m_y, -m_x

   0   0  -1    0
   0   1   0   3/4
   1   0   0   3/4

4^- (0,3/4,0) -3/8,y,3/8 -1

{ 4'^-₀₁₀ | 0 3/4 3/4 }

-y, x+3/4, z+3/4, -1
m_y, -m_x, -m_z

   0  -1   0    0
   1   0   0   3/4
   0   0   1   3/4

4⁺ (0,0,3/4) -3/8,3/8,z -1

{ 4'⁺₀₀₁ | 0 3/4 3/4 }

y+1/4, -x+1/2, z+3/4, -1
-m_y, m_x, -m_z

   0   1   0   1/4
  -1   0   0   1/2
   0   0   1   3/4

4^- (0,0,3/4) 3/8,1/8,z -1

{ 4'^-₀₀₁ | 1/4 1/2 3/4 }

y+1/4, x+3/4, -z+1/2, -1
-m_y, -m_x, m_z

   0   1   0   1/4
   1   0   0   3/4
   0   0  -1   1/2

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

{ 2'₁₁₀ | 1/4 3/4 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

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

{ 2'_1-10 | 0 1/2 1/2 }

-x, z+3/4, y+3/4, -1
m_x, -m_z, -m_y

  -1   0   0    0
   0   0   1   3/4
   0   1   0   3/4

2 (0,3/4,3/4) 0,y,y -1

{ 2'₀₁₁ | 0 3/4 3/4 }

-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,y+1/2,-y -1

{ 2'_01-1 | 0 1/2 1/2 }

z+1/4, -y+1/2, x+3/4, -1
-m_z, m_y, -m_x

   0   0   1   1/4
   0  -1   0   1/2
   1   0   0   3/4

2 (1/2,0,1/2) x-0.25,1/4,x -1

{ 2'₁₀₁ | 1/4 1/2 3/4 }

-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

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

{ 2'_-101 | 0 1/2 1/2 }

-x+1/4, z+1/2, -y+3/4, -1
-m_x,m_z,-m_y

  -1   0   0   1/4
   0   0   1   1/2
   0  -1   0   3/4

-4⁺ x,5/8,1/8 1/8,5/8,1/8 -1

{ -4'⁺₁₀₀ | 1/4 1/2 3/4 }

-x+1/4, -z+3/4, y+1/2, -1
-m_x,-m_z,m_y

  -1   0   0   1/4
   0   0  -1   3/4
   0   1   0   1/2

-4^- x,1/8,5/8 1/8,1/8,5/8 -1

{ -4'^-₁₀₀ | 1/4 3/4 1/2 }

-z+1/4, -y+3/4, x+1/2, -1
-m_z,-m_y,m_x

   0   0  -1   1/4
   0  -1   0   3/4
   1   0   0   1/2

-4⁺ -1/8,y,3/8 -1/8,3/8,3/8 -1

{ -4'⁺₀₁₀ | 1/4 3/4 1/2 }

z, -y+3/4, -x+3/4, -1
m_z,-m_y,-m_x

   0   0   1    0
   0  -1   0   3/4
  -1   0   0   3/4

-4^- 3/8,y,3/8 3/8,3/8,3/8 -1

{ -4'^-₀₁₀ | 0 3/4 3/4 }

y, -x+3/4, -z+3/4, -1
m_y,-m_x,-m_z

   0   1   0    0
  -1   0   0   3/4
   0   0  -1   3/4

-4⁺ 3/8,3/8,z 3/8,3/8,3/8 -1

{ -4'⁺₀₀₁ | 0 3/4 3/4 }

-y+1/4, x+1/2, -z+3/4, -1
-m_y,m_x,-m_z

   0  -1   0   1/4
   1   0   0   1/2
   0   0  -1   3/4

-4^- -1/8,3/8,z -1/8,3/8,3/8 -1

{ -4'^-₀₀₁ | 1/4 1/2 3/4 }

-y+1/4, -x+3/4, z+1/2, -1
-m_y,-m_x,m_z

   0  -1   0   1/4
  -1   0   0   3/4
   0   0   1   1/2

g (-1/4,1/4,1/2) x+1/2,-x,z -1

{ m'₁₁₀ | 1/4 3/4 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

g (1/4,1/4,1/2) x-0.25,x,z -1

{ m'_1-10 | 0 1/2 1/2 }

x, -z+3/4, -y+3/4, -1
m_x,-m_z,-m_y

   1   0   0    0
   0   0  -1   3/4
   0  -1   0   3/4

m x,y+3/4,-y -1

{ m'₀₁₁ | 0 3/4 3/4 }

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

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

{ m'_01-1 | 0 1/2 1/2 }

-z+1/4, y+1/2, -x+3/4, -1
-m_z,m_y,-m_x

   0   0  -1   1/4
   0   1   0   1/2
  -1   0   0   3/4

g (-1/4,1/2,1/4) -x+1/2,y,x -1

{ m'₁₀₁ | 1/4 1/2 3/4 }

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

g (1/4,1/2,1/4) x-0.25,y,x -1

{ m'_-101 | 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

t (1/2,0,1/2) +1

{ 1 | 1/2 0 1/2 }

x+1/2, -y+1/4, -z+3/4, +1
m_x,-m_y,-m_z

   1   0   0   1/2
   0  -1   0   1/4
   0   0  -1   3/4

2 (1/2,0,0) x,1/8,3/8 +1

{ 2₁₀₀ | 1/2 1/4 3/4 }

-x+3/4, y, -z+3/4, +1
-m_x,m_y,-m_z

  -1   0   0   3/4
   0   1   0    0
   0   0  -1   3/4

2 3/8,y,3/8 +1

{ 2₀₁₀ | 3/4 0 3/4 }

100

-x+3/4, -y+1/4, z+1/2, +1
-m_x,-m_y,m_z

  -1   0   0   3/4
   0  -1   0   1/4
   0   0   1   1/2

2 (0,0,1/2) 3/8,1/8,z +1

{ 2₀₀₁ | 3/4 1/4 1/2 }

101

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⁺ (1/3,1/3,1/3) x+1/6,x-1/6,x +1

{ 3⁺₁₁₁ | 1/2 0 1/2 }

102

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^- (1/3,1/3,1/3) x-0.16667,x-1/3,x +1

{ 3^-₁₁₁ | 1/2 0 1/2 }

103

-y+3/4, z, -x+3/4, +1
-m_y,m_z,-m_x

   0  -1   0   3/4
   0   0   1    0
  -1   0   0   3/4

3^- x+3/4,-x,-x +1

{ 3^-_1-1-1 | 3/4 0 3/4 }

104

-z+3/4, -x+1/4, y+1/2, +1
-m_z,-m_x,m_y

   0   0  -1   3/4
  -1   0   0   1/4
   0   1   0   1/2

3⁺ x+3/4,-x,-x +1

{ 3⁺_1-1-1 | 3/4 1/4 1/2 }

105

-y+3/4, -z+1/4, x+1/2, +1
-m_y,-m_z,m_x

   0  -1   0   3/4
   0   0  -1   1/4
   1   0   0   1/2

3^- (1/3,-1/3,1/3) -x-1/6,x+7/12,-x +1

{ 3^-_-11-1 | 3/4 1/4 1/2 }

106

z+1/2, -x+1/4, -y+3/4, +1
m_z,-m_x,-m_y

   0   0   1   1/2
  -1   0   0   1/4
   0  -1   0   3/4

3⁺ (1/3,-1/3,1/3) -x+1/6,x+5/12,-x +1

{ 3⁺_-11-1 | 1/2 1/4 3/4 }

107

y+1/2, -z+1/4, -x+3/4, +1
m_y,-m_z,-m_x

   0   1   0   1/2
   0   0  -1   1/4
  -1   0   0   3/4

3^- -x+3/4,-x+1/4,x +1

{ 3^-_-1-11 | 1/2 1/4 3/4 }

108

-z+3/4, x, -y+3/4, +1
-m_z,m_x,-m_y

   0   0  -1   3/4
   1   0   0    0
   0  -1   0   3/4

3⁺ -x+3/4,-x+3/4,x +1

{ 3⁺_-1-11 | 3/4 0 3/4 }

109

-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

-1 1/4,0,1/4 +1

{ -1 | 1/2 0 1/2 }

110

-x+1/2, y+1/4, z+3/4, +1
m_x, -m_y, -m_z

  -1   0   0   1/2
   0   1   0   1/4
   0   0   1   3/4

d (0,1/4,3/4) 1/4,y,z +1

{ m₁₀₀ | 1/2 1/4 3/4 }

111

x+3/4, -y, z+3/4, +1
-m_x, m_y, -m_z

   1   0   0   3/4
   0  -1   0    0
   0   0   1   3/4

d (3/4,0,3/4) x,0,z +1

{ m₀₁₀ | 3/4 0 3/4 }

112

x+3/4, y+1/4, -z+1/2, +1
-m_x, -m_y, m_z

   1   0   0   3/4
   0   1   0   1/4
   0   0  -1   1/2

d (3/4,1/4,0) x,y,1/4 +1

{ m₀₀₁ | 3/4 1/4 1/2 }

113

-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-0.5,x-1/2,x 0,0,1/2 +1

{ -3⁺₁₁₁ | 1/2 0 1/2 }

114

-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 1/2,0,0 +1

{ -3^-₁₁₁ | 1/2 0 1/2 }

115

y+3/4, -z, x+3/4, +1
-m_y, m_z, -m_x

   0   1   0   3/4
   0   0  -1    0
   1   0   0   3/4

-3^- x+3/4,-x,-x 0,-3/4,3/4 +1

{ -3^-_1-1-1 | 3/4 0 3/4 }

116

z+3/4, x+1/4, -y+1/2, +1
-m_z, -m_x, m_y

   0   0   1   3/4
   1   0   0   1/4
   0  -1   0   1/2

-3⁺ x+1/4,-x+1,-x 1/2,3/4,-1/4 +1

{ -3⁺_1-1-1 | 3/4 1/4 1/2 }

117

y+3/4, z+1/4, -x+1/2, +1
-m_y, -m_z, m_x

   0   1   0   3/4
   0   0   1   1/4
  -1   0   0   1/2

-3^- -x+1,x-1/4,-x 3/4,0,-1/4 +1

{ -3^-_-11-1 | 3/4 1/4 1/2 }

118

-z+1/2, x+1/4, y+3/4, +1
m_z, -m_x, -m_y

   0   0  -1   1/2
   1   0   0   1/4
   0   1   0   3/4

-3⁺ -x-1,x+3/4,-x -1/4,0,3/4 +1

{ -3⁺_-11-1 | 1/2 1/4 3/4 }

119

-y+1/2, z+1/4, x+3/4, +1
m_y, -m_z, -m_x

   0  -1   0   1/2
   0   0   1   1/4
   1   0   0   3/4

-3^- -x+1/4,-x+5/4,x -1/4,3/4,1/2 +1

{ -3^-_-1-11 | 1/2 1/4 3/4 }

120

z+3/4, -x, y+3/4, +1
-m_z, m_x, -m_y

   0   0   1   3/4
  -1   0   0    0
   0   1   0   3/4

-3⁺ -x+3/4,-x,x 3/4,-3/4,0 +1

{ -3⁺_-1-11 | 3/4 0 3/4 }

121

x+3/4, -z, y+3/4, -1
-m_x, m_z, -m_y

   1   0   0   3/4
   0   0  -1    0
   0   1   0   3/4

4⁺ (3/4,0,0) x,-3/8,3/8 -1

{ 4'⁺₁₀₀ | 3/4 0 3/4 }

122

x+3/4, z+1/4, -y+1/2, -1
-m_x, -m_z, m_y

   1   0   0   3/4
   0   0   1   1/4
   0  -1   0   1/2

4^- (3/4,0,0) x,3/8,1/8 -1

{ 4'^-₁₀₀ | 3/4 1/4 1/2 }

123

z+3/4, y+1/4, -x+1/2, -1
-m_z, -m_y, m_x

   0   0   1   3/4
   0   1   0   1/4
  -1   0   0   1/2

4⁺ (0,1/4,0) 5/8,y,-1/8 -1

{ 4'⁺₀₁₀ | 3/4 1/4 1/2 }

124

-z+1/2, y+1/4, x+3/4, -1
m_z, -m_y, -m_x

   0   0  -1   1/2
   0   1   0   1/4
   1   0   0   3/4

4^- (0,1/4,0) -1/8,y,5/8 -1

{ 4'^-₀₁₀ | 1/2 1/4 3/4 }

125

-y+1/2, x+1/4, z+3/4, -1
m_y, -m_x, -m_z

   0  -1   0   1/2
   1   0   0   1/4
   0   0   1   3/4

4⁺ (0,0,3/4) 1/8,3/8,z -1

{ 4'⁺₀₀₁ | 1/2 1/4 3/4 }

126

y+3/4, -x, z+3/4, -1
-m_y, m_x, -m_z

   0   1   0   3/4
  -1   0   0    0
   0   0   1   3/4

4^- (0,0,3/4) 3/8,-3/8,z -1

{ 4'^-₀₀₁ | 3/4 0 3/4 }

127

y+3/4, x+1/4, -z+1/2, -1
-m_y, -m_x, m_z

   0   1   0   3/4
   1   0   0   1/4
   0   0  -1   1/2

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

{ 2'₁₁₀ | 3/4 1/4 1/2 }

128

-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

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

{ 2'_1-10 | 1/2 0 1/2 }

129

-x+1/2, z+1/4, y+3/4, -1
m_x, -m_z, -m_y

  -1   0   0   1/2
   0   0   1   1/4
   0   1   0   3/4

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

{ 2'₀₁₁ | 1/2 1/4 3/4 }

130

-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

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

{ 2'_01-1 | 1/2 0 1/2 }

131

z+3/4, -y, x+3/4, -1
-m_z, m_y, -m_x

   0   0   1   3/4
   0  -1   0    0
   1   0   0   3/4

2 (3/4,0,3/4) x,0,x -1

{ 2'₁₀₁ | 3/4 0 3/4 }

132

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

{ 2'_-101 | 1/2 0 1/2 }

133

-x+3/4, z, -y+3/4, -1
-m_x,m_z,-m_y

  -1   0   0   3/4
   0   0   1    0
   0  -1   0   3/4

-4⁺ x,3/8,3/8 3/8,3/8,3/8 -1

{ -4'⁺₁₀₀ | 3/4 0 3/4 }

134

-x+3/4, -z+1/4, y+1/2, -1
-m_x,-m_z,m_y

  -1   0   0   3/4
   0   0  -1   1/4
   0   1   0   1/2

-4^- x,-1/8,3/8 3/8,-1/8,3/8 -1

{ -4'^-₁₀₀ | 3/4 1/4 1/2 }

135

-z+3/4, -y+1/4, x+1/2, -1
-m_z,-m_y,m_x

   0   0  -1   3/4
   0  -1   0   1/4
   1   0   0   1/2

-4⁺ 1/8,y,5/8 1/8,1/8,5/8 -1

{ -4'⁺₀₁₀ | 3/4 1/4 1/2 }

136

z+1/2, -y+1/4, -x+3/4, -1
m_z,-m_y,-m_x

   0   0   1   1/2
   0  -1   0   1/4
  -1   0   0   3/4

-4^- 5/8,y,1/8 5/8,1/8,1/8 -1

{ -4'^-₀₁₀ | 1/2 1/4 3/4 }

137

y+1/2, -x+1/4, -z+3/4, -1
m_y,-m_x,-m_z

   0   1   0   1/2
  -1   0   0   1/4
   0   0  -1   3/4

-4⁺ 3/8,-1/8,z 3/8,-1/8,3/8 -1

{ -4'⁺₀₀₁ | 1/2 1/4 3/4 }

138

-y+3/4, x, -z+3/4, -1
-m_y,m_x,-m_z

   0  -1   0   3/4
   1   0   0    0
   0   0  -1   3/4

-4^- 3/8,3/8,z 3/8,3/8,3/8 -1

{ -4'^-₀₀₁ | 3/4 0 3/4 }

139

-y+3/4, -x+1/4, z+1/2, -1
-m_y,-m_x,m_z

   0  -1   0   3/4
  -1   0   0   1/4
   0   0   1   1/2

g (1/4,-1/4,1/2) x+1/2,-x,z -1

{ m'₁₁₀ | 3/4 1/4 1/2 }

140

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

g (1/4,1/4,1/2) x+1/4,x,z -1

{ m'_1-10 | 1/2 0 1/2 }

141

x+1/2, -z+1/4, -y+3/4, -1
m_x,-m_z,-m_y

   1   0   0   1/2
   0   0  -1   1/4
   0  -1   0   3/4

g (1/2,-1/4,1/4) x,y+1/2,-y -1

{ m'₀₁₁ | 1/2 1/4 3/4 }

142

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

g (1/2,1/4,1/4) x,y-1/4,y -1

{ m'_01-1 | 1/2 0 1/2 }

143

-z+3/4, y, -x+3/4, -1
-m_z,m_y,-m_x

   0   0  -1   3/4
   0   1   0    0
  -1   0   0   3/4

m -x+3/4,y,x -1

{ m'₁₀₁ | 3/4 0 3/4 }

144

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

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

{ m'_-101 | 1/2 0 1/2 }

145

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

t (1/2,1/2,0) +1

{ 1 | 1/2 1/2 0 }

146

x+1/2, -y+3/4, -z+1/4, +1
m_x,-m_y,-m_z

   1   0   0   1/2
   0  -1   0   3/4
   0   0  -1   1/4

2 (1/2,0,0) x,3/8,1/8 +1

{ 2₁₀₀ | 1/2 3/4 1/4 }

147

-x+3/4, y+1/2, -z+1/4, +1
-m_x,m_y,-m_z

  -1   0   0   3/4
   0   1   0   1/2
   0   0  -1   1/4

2 (0,1/2,0) 3/8,y,1/8 +1

{ 2₀₁₀ | 3/4 1/2 1/4 }

148

-x+3/4, -y+3/4, z, +1
-m_x,-m_y,m_z

  -1   0   0   3/4
   0  -1   0   3/4
   0   0   1    0

2 3/8,3/8,z +1

{ 2₀₀₁ | 3/4 3/4 0 }

149

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⁺ (1/3,1/3,1/3) x+1/6,x+1/3,x +1

{ 3⁺₁₁₁ | 1/2 1/2 0 }

150

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^- (1/3,1/3,1/3) x+1/3,x+1/6,x +1

{ 3^-₁₁₁ | 1/2 1/2 0 }

151

-y+3/4, z+1/2, -x+1/4, +1
-m_y,m_z,-m_x

   0  -1   0   3/4
   0   0   1   1/2
  -1   0   0   1/4

3^- x+1/4,-x+1/2,-x +1

{ 3^-_1-1-1 | 3/4 1/2 1/4 }

152

-z+3/4, -x+3/4, y, +1
-m_z,-m_x,m_y

   0   0  -1   3/4
  -1   0   0   3/4
   0   1   0    0

3⁺ x+3/4,-x,-x +1

{ 3⁺_1-1-1 | 3/4 3/4 0 }

153

-y+3/4, -z+3/4, x, +1
-m_y,-m_z,m_x

   0  -1   0   3/4
   0   0  -1   3/4
   1   0   0    0

3^- -x,x+3/4,-x +1

{ 3^-_-11-1 | 3/4 3/4 0 }

154

z+1/2, -x+3/4, -y+1/4, +1
m_z,-m_x,-m_y

   0   0   1   1/2
  -1   0   0   3/4
   0  -1   0   1/4

3⁺ -x+1/2,x+1/4,-x +1

{ 3⁺_-11-1 | 1/2 3/4 1/4 }

155

y+1/2, -z+3/4, -x+1/4, +1
m_y,-m_z,-m_x

   0   1   0   1/2
   0   0  -1   3/4
  -1   0   0   1/4

3^- (1/3,1/3,-1/3) -x+7/12,-x+5/12,x +1

{ 3^-_-1-11 | 1/2 3/4 1/4 }

156

-z+3/4, x+1/2, -y+1/4, +1
-m_z,m_x,-m_y

   0   0  -1   3/4
   1   0   0   1/2
   0  -1   0   1/4

3⁺ (1/3,1/3,-1/3) -x+5/12,-x+7/12,x +1

{ 3⁺_-1-11 | 3/4 1/2 1/4 }

157

-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

-1 1/4,1/4,0 +1

{ -1 | 1/2 1/2 0 }

158

-x+1/2, y+3/4, z+1/4, +1
m_x, -m_y, -m_z

  -1   0   0   1/2
   0   1   0   3/4
   0   0   1   1/4

d (0,3/4,1/4) 1/4,y,z +1

{ m₁₀₀ | 1/2 3/4 1/4 }

159

x+3/4, -y+1/2, z+1/4, +1
-m_x, m_y, -m_z

   1   0   0   3/4
   0  -1   0   1/2
   0   0   1   1/4

d (3/4,0,1/4) x,1/4,z +1

{ m₀₁₀ | 3/4 1/2 1/4 }

160

x+3/4, y+3/4, -z, +1
-m_x, -m_y, m_z

   1   0   0   3/4
   0   1   0   3/4
   0   0  -1    0

d (3/4,3/4,0) x,y,0 +1

{ m₀₀₁ | 3/4 3/4 0 }

161

-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 1/2,0,0 +1

{ -3⁺₁₁₁ | 1/2 1/2 0 }

162

-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 0,1/2,0 +1

{ -3^-₁₁₁ | 1/2 1/2 0 }

163

y+3/4, -z+1/2, x+1/4, +1
-m_y, m_z, -m_x

   0   1   0   3/4
   0   0  -1   1/2
   1   0   0   1/4

-3^- x+5/4,-x,-x 1/2,-1/4,3/4 +1

{ -3^-_1-1-1 | 3/4 1/2 1/4 }

164

z+3/4, x+3/4, -y, +1
-m_z, -m_x, m_y

   0   0   1   3/4
   1   0   0   3/4
   0  -1   0    0

-3⁺ x-0.75,-x+3/2,-x 0,3/4,-3/4 +1

{ -3⁺_1-1-1 | 3/4 3/4 0 }

165

y+3/4, z+3/4, -x, +1
-m_y, -m_z, m_x

   0   1   0   3/4
   0   0   1   3/4
  -1   0   0    0

-3^- -x+3/2,x-3/4,-x 3/4,0,-3/4 +1

{ -3^-_-11-1 | 3/4 3/4 0 }

166

-z+1/2, x+3/4, y+1/4, +1
m_z, -m_x, -m_y

   0   0  -1   1/2
   1   0   0   3/4
   0   1   0   1/4

-3⁺ -x-1,x+5/4,-x -1/4,1/2,3/4 +1

{ -3⁺_-11-1 | 1/2 3/4 1/4 }

167

-y+1/2, z+3/4, x+1/4, +1
m_y, -m_z, -m_x

   0  -1   0   1/2
   0   0   1   3/4
   1   0   0   1/4

-3^- -x-1/4,-x+3/4,x -1/4,3/4,0 +1

{ -3^-_-1-11 | 1/2 3/4 1/4 }

168

z+3/4, -x+1/2, y+1/4, +1
-m_z, m_x, -m_y

   0   0   1   3/4
  -1   0   0   1/2
   0   1   0   1/4

-3⁺ -x+3/4,-x,x 3/4,-1/4,0 +1

{ -3⁺_-1-11 | 3/4 1/2 1/4 }

169

x+3/4, -z+1/2, y+1/4, -1
-m_x, m_z, -m_y

   1   0   0   3/4
   0   0  -1   1/2
   0   1   0   1/4

4⁺ (3/4,0,0) x,1/8,3/8 -1

{ 4'⁺₁₀₀ | 3/4 1/2 1/4 }

170

x+3/4, z+3/4, -y, -1
-m_x, -m_z, m_y

   1   0   0   3/4
   0   0   1   3/4
   0  -1   0    0

4^- (3/4,0,0) x,3/8,-3/8 -1

{ 4'^-₁₀₀ | 3/4 3/4 0 }

171

z+3/4, y+3/4, -x, -1
-m_z, -m_y, m_x

   0   0   1   3/4
   0   1   0   3/4
  -1   0   0    0

4⁺ (0,3/4,0) 3/8,y,-3/8 -1

{ 4'⁺₀₁₀ | 3/4 3/4 0 }

172

-z+1/2, y+3/4, x+1/4, -1
m_z, -m_y, -m_x

   0   0  -1   1/2
   0   1   0   3/4
   1   0   0   1/4

4^- (0,3/4,0) 1/8,y,3/8 -1

{ 4'^-₀₁₀ | 1/2 3/4 1/4 }

173

-y+1/2, x+3/4, z+1/4, -1
m_y, -m_x, -m_z

   0  -1   0   1/2
   1   0   0   3/4
   0   0   1   1/4

4⁺ (0,0,1/4) -1/8,5/8,z -1

{ 4'⁺₀₀₁ | 1/2 3/4 1/4 }

174

y+3/4, -x+1/2, z+1/4, -1
-m_y, m_x, -m_z

   0   1   0   3/4
  -1   0   0   1/2
   0   0   1   1/4

4^- (0,0,1/4) 5/8,-1/8,z -1

{ 4'^-₀₀₁ | 3/4 1/2 1/4 }

175

y+3/4, x+3/4, -z, -1
-m_y, -m_x, m_z

   0   1   0   3/4
   1   0   0   3/4
   0   0  -1    0

2 (3/4,3/4,0) x,x,0 -1

{ 2'₁₁₀ | 3/4 3/4 0 }

176

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

{ 2'_1-10 | 1/2 1/2 0 }

177

-x+1/2, z+3/4, y+1/4, -1
m_x, -m_z, -m_y

  -1   0   0   1/2
   0   0   1   3/4
   0   1   0   1/4

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

{ 2'₀₁₁ | 1/2 3/4 1/4 }

178

-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

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

{ 2'_01-1 | 1/2 1/2 0 }

179

z+3/4, -y+1/2, x+1/4, -1
-m_z, m_y, -m_x

   0   0   1   3/4
   0  -1   0   1/2
   1   0   0   1/4

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

{ 2'₁₀₁ | 3/4 1/2 1/4 }

180

-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

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

{ 2'_-101 | 1/2 1/2 0 }

181

-x+3/4, z+1/2, -y+1/4, -1
-m_x,m_z,-m_y

  -1   0   0   3/4
   0   0   1   1/2
   0  -1   0   1/4

-4⁺ x,3/8,-1/8 3/8,3/8,-1/8 -1

{ -4'⁺₁₀₀ | 3/4 1/2 1/4 }

182

-x+3/4, -z+3/4, y, -1
-m_x,-m_z,m_y

  -1   0   0   3/4
   0   0  -1   3/4
   0   1   0    0

-4^- x,3/8,3/8 3/8,3/8,3/8 -1

{ -4'^-₁₀₀ | 3/4 3/4 0 }

183

-z+3/4, -y+3/4, x, -1
-m_z,-m_y,m_x

   0   0  -1   3/4
   0  -1   0   3/4
   1   0   0    0

-4⁺ 3/8,y,3/8 3/8,3/8,3/8 -1

{ -4'⁺₀₁₀ | 3/4 3/4 0 }

184

z+1/2, -y+3/4, -x+1/4, -1
m_z,-m_y,-m_x

   0   0   1   1/2
   0  -1   0   3/4
  -1   0   0   1/4

-4^- 3/8,y,-1/8 3/8,3/8,-1/8 -1

{ -4'^-₀₁₀ | 1/2 3/4 1/4 }

185

y+1/2, -x+3/4, -z+1/4, -1
m_y,-m_x,-m_z

   0   1   0   1/2
  -1   0   0   3/4
   0   0  -1   1/4

-4⁺ 5/8,1/8,z 5/8,1/8,1/8 -1

{ -4'⁺₀₀₁ | 1/2 3/4 1/4 }

186

-y+3/4, x+1/2, -z+1/4, -1
-m_y,m_x,-m_z

   0  -1   0   3/4
   1   0   0   1/2
   0   0  -1   1/4

-4^- 1/8,5/8,z 1/8,5/8,1/8 -1

{ -4'^-₀₀₁ | 3/4 1/2 1/4 }

187

-y+3/4, -x+3/4, z, -1
-m_y,-m_x,m_z

   0  -1   0   3/4
  -1   0   0   3/4
   0   0   1    0

m x+3/4,-x,z -1

{ m'₁₁₀ | 3/4 3/4 0 }

188

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

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

{ m'_1-10 | 1/2 1/2 0 }

189

x+1/2, -z+3/4, -y+1/4, -1
m_x,-m_z,-m_y

   1   0   0   1/2
   0   0  -1   3/4
   0  -1   0   1/4

g (1/2,1/4,-1/4) x,y+1/2,-y -1

{ m'₀₁₁ | 1/2 3/4 1/4 }

190

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

g (1/2,1/4,1/4) x,y+1/4,y -1

{ m'_01-1 | 1/2 1/2 0 }

191

-z+3/4, y+1/2, -x+1/4, -1
-m_z,m_y,-m_x

   0   0  -1   3/4
   0   1   0   1/2
  -1   0   0   1/4

g (1/4,1/2,-1/4) -x+1/2,y,x -1

{ m'₁₀₁ | 3/4 1/2 1/4 }

192

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

g (1/4,1/2,1/4) x+1/4,y,x -1

{ m'_-101 | 1/2 1/2 0 }

Go to the list of the Wyckoff Positions of the Group Fd-3m' (#227.131)
Go to the Systematic Absences for the Group Fd-3m' (#227.131)

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General Positions of the Group Fd-3m' (#227.131) 227.131 Fd-3m' (UNI symbol)For this space group, BNS and OG settings coincide.Its label in the OG setting is given as: Fd-3m' (#227.4.1631)

General Positions of the Group Fd-3m' (#227.131)
**227.131 Fd-3m' (UNI symbol)**

For this space group, BNS and OG settings coincide.
Its label in the OG setting is given as: Fd-3m' (#227.4.1631)