129.99.1.1.L
Spin space group detail page with configuration, notation, nontrivial spin-space point group, spin-space point group, symmetry operations, and spin Wyckoff-position data.
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Configuration: Collinear
Type: type-t
G0 / L0: 129 / 99
Identifier: 129.99.1.1.L
it / ik: 2 / 1
Nontrivial spin-space point group: $-1$
Spin-space point group: $∞/mm$
International Notation: $$P\ce{^{1}{4/}}\ce{^{\text{-}1}{n}}\ce{^{1}{m}}\ce{^{1}{m}}\ce{^{\infty m}{1}}$$
Conventional to Primitive Matrix P:
$$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$
Note: (aC, bC, cC) P = (aP, bP, cP)
Transformation Matrix M:
$$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{4} \\ 0 & 1 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & 0\end{array}\right]$$
Note: [a_G0, b_G0, c_G0] M = [a_L0, b_L0, c_L0]
Translational group generators:
$$\begin{aligned}a &= (1, 0, 0) \\ b &= (0, 1, 0) \\ c &= (0, 0, 1)\end{aligned}$$
Note: The listed operations below are understood modulo the translational group generated by a, b, and c.
E.g. for 129.99.1.1.L, if a=(1, 0, 0), then (x, y, z) and (x+1, y, z) represent the same translation part.
E_E_tau
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
U_E_0
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{\ce{^{\infty}{1}}||1|0 0 0\right\}$ $(x,y,z,+1,\cos(\phi) u - \sin(\phi) v,\sin(\phi) u + \cos(\phi) v,w)$ $$\begin{bmatrix}\cos(\phi) & -\sin(\phi) & 0 \\ \sin(\phi) & \cos(\phi) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
3 $\left\{\ce{^{m_{100}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,-u,v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
U_E_tau
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
U_R_tau
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{1||4^{1}_{001}|\frac{1}{2} 0 0\right\}$ $(\frac{1}{2} - y,x,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
3 $\left\{-1||m_{001}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(x + \frac{1}{2},y + \frac{1}{2},-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
4 $\left\{1||m_{100}|\frac{1}{2} 0 0\right\}$ $(\frac{1}{2} - x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
5 $\left\{1||m_{110}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - y,\frac{1}{2} - x,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
6 $\left\{1||2_{001}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - x,\frac{1}{2} - y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
7 $\left\{-1||-4^{3}_{001}|0 \frac{1}{2} 0\right\}$ $(-y,x + \frac{1}{2},-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
8 $\left\{1||m_{010}|0 \frac{1}{2} 0\right\}$ $(x,\frac{1}{2} - y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
9 $\left\{1||4^{3}_{001}|0 \frac{1}{2} 0\right\}$ $(y,\frac{1}{2} - x,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ -1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
10 $\left\{-1||-1|0 0 0\right\}$ $(-x,-y,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
11 $\left\{1||m_{1-10}|0 0 0\right\}$ $(y,x,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
12 $\left\{-1||-4^{1}_{001}|\frac{1}{2} 0 0\right\}$ $(y + \frac{1}{2},-x,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
13 $\left\{-1||2_{010}|0 \frac{1}{2} 0\right\}$ $(-x,y + \frac{1}{2},-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
14 $\left\{-1||2_{1-10}|0 0 0\right\}$ $(-y,-x,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
15 $\left\{-1||2_{100}|\frac{1}{2} 0 0\right\}$ $(x + \frac{1}{2},-y,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
16 $\left\{-1||2_{110}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(y + \frac{1}{2},x + \frac{1}{2},-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
No.
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{1||4^{1}_{001}|\frac{1}{2} 0 0\right\}$ $(\frac{1}{2} - y,x,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
3 $\left\{-1||m_{001}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(x + \frac{1}{2},y + \frac{1}{2},-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
4 $\left\{1||m_{100}|\frac{1}{2} 0 0\right\}$ $(\frac{1}{2} - x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
5 $\left\{1||m_{110}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - y,\frac{1}{2} - x,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
6 $\left\{1||2_{001}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - x,\frac{1}{2} - y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
7 $\left\{-1||-4^{3}_{001}|0 \frac{1}{2} 0\right\}$ $(-y,x + \frac{1}{2},-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
8 $\left\{1||m_{010}|0 \frac{1}{2} 0\right\}$ $(x,\frac{1}{2} - y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
9 $\left\{1||4^{3}_{001}|0 \frac{1}{2} 0\right\}$ $(y,\frac{1}{2} - x,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ -1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
10 $\left\{-1||-1|0 0 0\right\}$ $(-x,-y,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
11 $\left\{1||m_{1-10}|0 0 0\right\}$ $(y,x,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
12 $\left\{-1||-4^{1}_{001}|\frac{1}{2} 0 0\right\}$ $(y + \frac{1}{2},-x,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
13 $\left\{-1||2_{010}|0 \frac{1}{2} 0\right\}$ $(-x,y + \frac{1}{2},-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
14 $\left\{-1||2_{1-10}|0 0 0\right\}$ $(-y,-x,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
15 $\left\{-1||2_{100}|\frac{1}{2} 0 0\right\}$ $(x + \frac{1}{2},-y,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
16 $\left\{-1||2_{110}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(y + \frac{1}{2},x + \frac{1}{2},-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{\infty}{1}}||1|0 0 0\right\}$ $(x,y,z,+1,\cos(\phi) u - \sin(\phi) v,\sin(\phi) u + \cos(\phi) v,w)$ $$\begin{bmatrix}\cos(\phi) & -\sin(\phi) & 0 \\ \sin(\phi) & \cos(\phi) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{\ce{^{m_{100}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,-u,v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
wyckoff position site symmetry Coordinates
$(0,0,0\mid mx,my,mz)$
16k $(x,y,z\mid 0,0,mx),(\frac{1}{2} - x,\frac{1}{2} - y,z\mid 0,0,mx),(\frac{1}{2} - y,x,z\mid 0,0,mx),(y,\frac{1}{2} - x,z\mid 0,0,mx),(-x,y + \frac{1}{2},-z\mid 0,0,-mx),(x + \frac{1}{2},-y,-z\mid 0,0,-mx),(y + \frac{1}{2},x + \frac{1}{2},-z\mid 0,0,-mx),(-y,-x,-z\mid 0,0,-mx),(-x,-y,-z\mid 0,0,-mx),(x + \frac{1}{2},y + \frac{1}{2},-z\mid 0,0,-mx),(y + \frac{1}{2},-x,-z\mid 0,0,-mx),(-y,x + \frac{1}{2},-z\mid 0,0,-mx),(x,\frac{1}{2} - y,z\mid 0,0,mx),(\frac{1}{2} - x,y,z\mid 0,0,mx),(\frac{1}{2} - y,\frac{1}{2} - x,z\mid 0,0,mx),(y,x,z\mid 0,0,mx)$
8j $(x,x,z\mid 0,0,mx),(\frac{1}{2} - x,\frac{1}{2} - x,z\mid 0,0,mx),(\frac{1}{2} - x,x,z\mid 0,0,mx),(x,\frac{1}{2} - x,z\mid 0,0,mx),(-x,x + \frac{1}{2},-z\mid 0,0,-mx),(x + \frac{1}{2},-x,-z\mid 0,0,-mx),(x + \frac{1}{2},x + \frac{1}{2},-z\mid 0,0,-mx),(-x,-x,-z\mid 0,0,-mx)$
8i $(\frac{1}{4},y,z\mid 0,0,mx),(\frac{1}{4},\frac{1}{2} - y,z\mid 0,0,mx),(\frac{1}{2} - y,\frac{1}{4},z\mid 0,0,mx),(y,\frac{1}{4},z\mid 0,0,mx),(\frac{3}{4},y + \frac{1}{2},-z\mid 0,0,-mx),(\frac{3}{4},-y,-z\mid 0,0,-mx),(y + \frac{1}{2},\frac{3}{4},-z\mid 0,0,-mx),(-y,\frac{3}{4},-z\mid 0,0,-mx)$
8h $(x,-x,\frac{1}{2}\mid 0,0,0),(\frac{1}{2} - x,x + \frac{1}{2},\frac{1}{2}\mid 0,0,0),(x + \frac{1}{2},x,\frac{1}{2}\mid 0,0,0),(-x,\frac{1}{2} - x,\frac{1}{2}\mid 0,0,0),(-x,x,\frac{1}{2}\mid 0,0,0),(x + \frac{1}{2},\frac{1}{2} - x,\frac{1}{2}\mid 0,0,0),(\frac{1}{2} - x,-x,\frac{1}{2}\mid 0,0,0),(x,x + \frac{1}{2},\frac{1}{2}\mid 0,0,0)$
8g $(x,-x,0\mid 0,0,0),(\frac{1}{2} - x,x + \frac{1}{2},0\mid 0,0,0),(x + \frac{1}{2},x,0\mid 0,0,0),(-x,\frac{1}{2} - x,0\mid 0,0,0),(-x,x,0\mid 0,0,0),(x + \frac{1}{2},\frac{1}{2} - x,0\mid 0,0,0),(\frac{1}{2} - x,-x,0\mid 0,0,0),(x,x + \frac{1}{2},0\mid 0,0,0)$
4f $(\frac{3}{4},\frac{1}{4},z\mid 0,0,mx),(\frac{1}{4},\frac{3}{4},z\mid 0,0,mx),(\frac{1}{4},\frac{3}{4},-z\mid 0,0,-mx),(\frac{3}{4},\frac{1}{4},-z\mid 0,0,-mx)$
4e $(0,0,\frac{1}{2}\mid 0,0,0),(\frac{1}{2},\frac{1}{2},\frac{1}{2}\mid 0,0,0),(\frac{1}{2},0,\frac{1}{2}\mid 0,0,0),(0,\frac{1}{2},\frac{1}{2}\mid 0,0,0)$
4d $(0,0,0\mid 0,0,0),(\frac{1}{2},\frac{1}{2},0\mid 0,0,0),(\frac{1}{2},0,0\mid 0,0,0),(0,\frac{1}{2},0\mid 0,0,0)$
2c $(\frac{1}{4},\frac{1}{4},z\mid 0,0,mx),(\frac{3}{4},\frac{3}{4},-z\mid 0,0,-mx)$
2b $(\frac{3}{4},\frac{1}{4},\frac{1}{2}\mid 0,0,0),(\frac{1}{4},\frac{3}{4},\frac{1}{2}\mid 0,0,0)$
2a $(\frac{3}{4},\frac{1}{4},0\mid 0,0,0),(\frac{1}{4},\frac{3}{4},0\mid 0,0,0)$
Site symmetry: $^{1}1^{\infty m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{\infty}{1}}||1|0 0 0\right\}$ $(x,y,z,+1,\cos(\phi) u - \sin(\phi) v,\sin(\phi) u + \cos(\phi) v,w)$ $$\begin{bmatrix}\cos(\phi) & -\sin(\phi) & 0 \\ \sin(\phi) & \cos(\phi) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{\ce{^{m_{100}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,-u,v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $..^{1}m^{\infty m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
11 $\left\{1||m_{1-10}|0 0 0\right\}$ $(y,x,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{\infty}{1}}||1|0 0 0\right\}$ $(x,y,z,+1,\cos(\phi) u - \sin(\phi) v,\sin(\phi) u + \cos(\phi) v,w)$ $$\begin{bmatrix}\cos(\phi) & -\sin(\phi) & 0 \\ \sin(\phi) & \cos(\phi) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{\ce{^{m_{100}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,-u,v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $.^{1}m.^{\infty m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
4 $\left\{1||m_{100}|\frac{1}{2} 0 0\right\}$ $(\frac{1}{2} - x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{\infty}{1}}||1|0 0 0\right\}$ $(x,y,z,+1,\cos(\phi) u - \sin(\phi) v,\sin(\phi) u + \cos(\phi) v,w)$ $$\begin{bmatrix}\cos(\phi) & -\sin(\phi) & 0 \\ \sin(\phi) & \cos(\phi) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{\ce{^{m_{100}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,-u,v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $..^{\!-\!1}2^{\infty m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
14 $\left\{-1||2_{1-10}|0 0 0\right\}$ $(-y,-x,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{\infty}{1}}||1|0 0 0\right\}$ $(x,y,z,+1,\cos(\phi) u - \sin(\phi) v,\sin(\phi) u + \cos(\phi) v,w)$ $$\begin{bmatrix}\cos(\phi) & -\sin(\phi) & 0 \\ \sin(\phi) & \cos(\phi) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{\ce{^{m_{100}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,-u,v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $..^{\!-\!1}2^{\infty m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
14 $\left\{-1||2_{1-10}|0 0 0\right\}$ $(-y,-x,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{\infty}{1}}||1|0 0 0\right\}$ $(x,y,z,+1,\cos(\phi) u - \sin(\phi) v,\sin(\phi) u + \cos(\phi) v,w)$ $$\begin{bmatrix}\cos(\phi) & -\sin(\phi) & 0 \\ \sin(\phi) & \cos(\phi) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{\ce{^{m_{100}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,-u,v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $^{1}2^{1}m^{1}m .^{\infty m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
4 $\left\{1||m_{100}|\frac{1}{2} 0 0\right\}$ $(\frac{1}{2} - x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
6 $\left\{1||2_{001}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - x,\frac{1}{2} - y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
8 $\left\{1||m_{010}|0 \frac{1}{2} 0\right\}$ $(x,\frac{1}{2} - y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{\infty}{1}}||1|0 0 0\right\}$ $(x,y,z,+1,\cos(\phi) u - \sin(\phi) v,\sin(\phi) u + \cos(\phi) v,w)$ $$\begin{bmatrix}\cos(\phi) & -\sin(\phi) & 0 \\ \sin(\phi) & \cos(\phi) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{\ce{^{m_{100}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,-u,v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $..^{\!-\!1}2/^{1}m^{\infty m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
10 $\left\{-1||-1|0 0 0\right\}$ $(-x,-y,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
11 $\left\{1||m_{1-10}|0 0 0\right\}$ $(y,x,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
14 $\left\{-1||2_{1-10}|0 0 0\right\}$ $(-y,-x,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{\infty}{1}}||1|0 0 0\right\}$ $(x,y,z,+1,\cos(\phi) u - \sin(\phi) v,\sin(\phi) u + \cos(\phi) v,w)$ $$\begin{bmatrix}\cos(\phi) & -\sin(\phi) & 0 \\ \sin(\phi) & \cos(\phi) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{\ce{^{m_{100}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,-u,v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $..^{\!-\!1}2/^{1}m^{\infty m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
10 $\left\{-1||-1|0 0 0\right\}$ $(-x,-y,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
11 $\left\{1||m_{1-10}|0 0 0\right\}$ $(y,x,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
14 $\left\{-1||2_{1-10}|0 0 0\right\}$ $(-y,-x,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{\infty}{1}}||1|0 0 0\right\}$ $(x,y,z,+1,\cos(\phi) u - \sin(\phi) v,\sin(\phi) u + \cos(\phi) v,w)$ $$\begin{bmatrix}\cos(\phi) & -\sin(\phi) & 0 \\ \sin(\phi) & \cos(\phi) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{\ce{^{m_{100}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,-u,v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $^{1}4^{1}m^{1}m^{\infty m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{1||4^{1}_{001}|\frac{1}{2} 0 0\right\}$ $(\frac{1}{2} - y,x,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
4 $\left\{1||m_{100}|\frac{1}{2} 0 0\right\}$ $(\frac{1}{2} - x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
5 $\left\{1||m_{110}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - y,\frac{1}{2} - x,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
6 $\left\{1||2_{001}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - x,\frac{1}{2} - y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
8 $\left\{1||m_{010}|0 \frac{1}{2} 0\right\}$ $(x,\frac{1}{2} - y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
9 $\left\{1||4^{3}_{001}|0 \frac{1}{2} 0\right\}$ $(y,\frac{1}{2} - x,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ -1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
11 $\left\{1||m_{1-10}|0 0 0\right\}$ $(y,x,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{\infty}{1}}||1|0 0 0\right\}$ $(x,y,z,+1,\cos(\phi) u - \sin(\phi) v,\sin(\phi) u + \cos(\phi) v,w)$ $$\begin{bmatrix}\cos(\phi) & -\sin(\phi) & 0 \\ \sin(\phi) & \cos(\phi) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{\ce{^{m_{100}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,-u,v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $^{\!-\!1}\!-\!4^{1}m^{\!-\!1}2^{\infty m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
4 $\left\{1||m_{100}|\frac{1}{2} 0 0\right\}$ $(\frac{1}{2} - x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
6 $\left\{1||2_{001}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - x,\frac{1}{2} - y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
7 $\left\{-1||-4^{3}_{001}|0 \frac{1}{2} 0\right\}$ $(-y,x + \frac{1}{2},-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
8 $\left\{1||m_{010}|0 \frac{1}{2} 0\right\}$ $(x,\frac{1}{2} - y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
12 $\left\{-1||-4^{1}_{001}|\frac{1}{2} 0 0\right\}$ $(y + \frac{1}{2},-x,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
14 $\left\{-1||2_{1-10}|0 0 0\right\}$ $(-y,-x,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
16 $\left\{-1||2_{110}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(y + \frac{1}{2},x + \frac{1}{2},-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{\infty}{1}}||1|0 0 0\right\}$ $(x,y,z,+1,\cos(\phi) u - \sin(\phi) v,\sin(\phi) u + \cos(\phi) v,w)$ $$\begin{bmatrix}\cos(\phi) & -\sin(\phi) & 0 \\ \sin(\phi) & \cos(\phi) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{\ce{^{m_{100}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,-u,v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $^{\!-\!1}\!-\!4^{1}m^{\!-\!1}2^{\infty m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
4 $\left\{1||m_{100}|\frac{1}{2} 0 0\right\}$ $(\frac{1}{2} - x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
6 $\left\{1||2_{001}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - x,\frac{1}{2} - y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
7 $\left\{-1||-4^{3}_{001}|0 \frac{1}{2} 0\right\}$ $(-y,x + \frac{1}{2},-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
8 $\left\{1||m_{010}|0 \frac{1}{2} 0\right\}$ $(x,\frac{1}{2} - y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
12 $\left\{-1||-4^{1}_{001}|\frac{1}{2} 0 0\right\}$ $(y + \frac{1}{2},-x,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
14 $\left\{-1||2_{1-10}|0 0 0\right\}$ $(-y,-x,-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
16 $\left\{-1||2_{110}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(y + \frac{1}{2},x + \frac{1}{2},-z,-1,-u,-v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{\infty}{1}}||1|0 0 0\right\}$ $(x,y,z,+1,\cos(\phi) u - \sin(\phi) v,\sin(\phi) u + \cos(\phi) v,w)$ $$\begin{bmatrix}\cos(\phi) & -\sin(\phi) & 0 \\ \sin(\phi) & \cos(\phi) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{\ce{^{m_{100}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,-u,v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$