63.28.6.1.P
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: Coplanar
Type: type-g
G0 / L0: 63 / 28
Identifier: 63.28.6.1.P
it / ik: 2 / 6
Nontrivial spin-space point group: $622$
Spin-space point group: $6/mmm$
International Notation: $$C\ce{^{2_{100}}{m}}\ce{^{1}{c}}\ce{^{1}{m}} \vert (3^{1}_{001},1,1;6^{1}_{001})\ce{^{m_{001}}{1}}$$
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:
$$\left[\begin{array}{ccc|c}0 & 0 & -3 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$
Note: [a_G0, b_G0, c_G0] M = [a_L0, b_L0, c_L0]
Translational group generators:
$$\begin{aligned}a &= (3, 0, 0) \\ b &= (0, 1, 0) \\ c &= (0, 0, 1)\end{aligned}$$
Note: The listed operations below are understood modulo the translational group generated by a, b, and c.
E.g. for 63.28.6.1.P, if a=(3, 0, 0), then (x, y, z) and (x+3, 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 $\left\{\ce{^{m_{001}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,u,v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
U_E_tau
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{3^{1}_{001}||1|1 0 0\right\}$ $(x + 1,y,z,+1,\cos(\frac{2\pi}{3}) u - \sin(\frac{2\pi}{3}) v,\sin(\frac{2\pi}{3}) u + \cos(\frac{2\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{2\pi}{3}) & -\sin(\frac{2\pi}{3}) & 0 \\ \sin(\frac{2\pi}{3}) & \cos(\frac{2\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
3 $\left\{6^{1}_{001}||1|\frac{1}{2} \frac{1}{2} 0\right\}$ $(x + \frac{1}{2},y + \frac{1}{2},z,+1,\cos(\frac{\pi}{3}) u - \sin(\frac{\pi}{3}) v,\sin(\frac{\pi}{3}) u + \cos(\frac{\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{\pi}{3}) & -\sin(\frac{\pi}{3}) & 0 \\ \sin(\frac{\pi}{3}) & \cos(\frac{\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
4 $\left\{3^{2}_{001}||1|2 0 0\right\}$ $(x + 2,y,z,+1,\cos(\frac{4\pi}{3}) u - \sin(\frac{4\pi}{3}) v,\sin(\frac{4\pi}{3}) u + \cos(\frac{4\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{4\pi}{3}) & -\sin(\frac{4\pi}{3}) & 0 \\ \sin(\frac{4\pi}{3}) & \cos(\frac{4\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
5 $\left\{2_{001}||1|\frac{3}{2} \frac{1}{2} 0\right\}$ $(x + \frac{3}{2},y + \frac{1}{2},z,+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{3}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
6 $\left\{6^{5}_{001}||1|\frac{5}{2} \frac{1}{2} 0\right\}$ $(x + \frac{5}{2},y + \frac{1}{2},z,+1,\cos(\frac{5\pi}{3}) u - \sin(\frac{5\pi}{3}) v,\sin(\frac{5\pi}{3}) u + \cos(\frac{5\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{5\pi}{3}) & -\sin(\frac{5\pi}{3}) & 0 \\ \sin(\frac{5\pi}{3}) & \cos(\frac{5\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{5}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
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 $\left\{2_{100}||m_{100}|0 0 0\right\}$ $(-x,y,z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
3 $\left\{1||m_{010}|0 0 \frac{1}{2}\right\}$ $(x,-y,z + \frac{1}{2},+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
4 $\left\{1||m_{001}|0 0 \frac{1}{2}\right\}$ $(x,y,\frac{1}{2} - z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
5 $\left\{2_{100}||2_{001}|0 0 \frac{1}{2}\right\}$ $(-x,-y,z + \frac{1}{2},+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
6 $\left\{2_{100}||2_{010}|0 0 \frac{1}{2}\right\}$ $(-x,y,\frac{1}{2} - z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
7 $\left\{1||2_{100}|0 0 0\right\}$ $(x,-y,-z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
8 $\left\{2_{100}||-1|0 0 0\right\}$ $(-x,-y,-z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
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 $\left\{1||m_{010}|0 0 \frac{1}{2}\right\}$ $(x,-y,z + \frac{1}{2},+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
3 $\left\{1||m_{001}|0 0 \frac{1}{2}\right\}$ $(x,y,\frac{1}{2} - z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
4 $\left\{6^{1}_{001}||1|\frac{1}{2} \frac{1}{2} 0\right\}$ $(x + \frac{1}{2},y + \frac{1}{2},z,+1,\cos(\frac{\pi}{3}) u - \sin(\frac{\pi}{3}) v,\sin(\frac{\pi}{3}) u + \cos(\frac{\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{\pi}{3}) & -\sin(\frac{\pi}{3}) & 0 \\ \sin(\frac{\pi}{3}) & \cos(\frac{\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
5 $\left\{3^{1}_{001}||1|1 0 0\right\}$ $(x + 1,y,z,+1,\cos(\frac{2\pi}{3}) u - \sin(\frac{2\pi}{3}) v,\sin(\frac{2\pi}{3}) u + \cos(\frac{2\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{2\pi}{3}) & -\sin(\frac{2\pi}{3}) & 0 \\ \sin(\frac{2\pi}{3}) & \cos(\frac{2\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
6 $\left\{2_{100}||m_{100}|0 0 0\right\}$ $(-x,y,z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
7 $\left\{1||2_{100}|0 0 0\right\}$ $(x,-y,-z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
8 $\left\{6^{1}_{001}||m_{010}|\frac{1}{2} \frac{1}{2} \frac{1}{2}\right\}$ $(x + \frac{1}{2},\frac{1}{2} - y,z + \frac{1}{2},+1,\cos(\frac{\pi}{3}) u - \sin(\frac{\pi}{3}) v,\sin(\frac{\pi}{3}) u + \cos(\frac{\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{\pi}{3}) & -\sin(\frac{\pi}{3}) & 0 \\ \sin(\frac{\pi}{3}) & \cos(\frac{\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
9 $\left\{3^{1}_{001}||m_{010}|1 0 \frac{1}{2}\right\}$ $(x + 1,-y,z + \frac{1}{2},+1,\cos(\frac{2\pi}{3}) u - \sin(\frac{2\pi}{3}) v,\sin(\frac{2\pi}{3}) u + \cos(\frac{2\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{2\pi}{3}) & -\sin(\frac{2\pi}{3}) & 0 \\ \sin(\frac{2\pi}{3}) & \cos(\frac{2\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 1 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
10 $\left\{2_{100}||2_{001}|0 0 \frac{1}{2}\right\}$ $(-x,-y,z + \frac{1}{2},+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
11 $\left\{6^{1}_{001}||m_{001}|\frac{1}{2} \frac{1}{2} \frac{1}{2}\right\}$ $(x + \frac{1}{2},y + \frac{1}{2},\frac{1}{2} - z,+1,\cos(\frac{\pi}{3}) u - \sin(\frac{\pi}{3}) v,\sin(\frac{\pi}{3}) u + \cos(\frac{\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{\pi}{3}) & -\sin(\frac{\pi}{3}) & 0 \\ \sin(\frac{\pi}{3}) & \cos(\frac{\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
12 $\left\{3^{1}_{001}||m_{001}|1 0 \frac{1}{2}\right\}$ $(x + 1,y,\frac{1}{2} - z,+1,\cos(\frac{2\pi}{3}) u - \sin(\frac{2\pi}{3}) v,\sin(\frac{2\pi}{3}) u + \cos(\frac{2\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{2\pi}{3}) & -\sin(\frac{2\pi}{3}) & 0 \\ \sin(\frac{2\pi}{3}) & \cos(\frac{2\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
13 $\left\{2_{100}||2_{010}|0 0 \frac{1}{2}\right\}$ $(-x,y,\frac{1}{2} - z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
14 $\left\{6^{1}_{001}||2_{100}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(x + \frac{1}{2},\frac{1}{2} - y,-z,+1,\cos(\frac{\pi}{3}) u - \sin(\frac{\pi}{3}) v,\sin(\frac{\pi}{3}) u + \cos(\frac{\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{\pi}{3}) & -\sin(\frac{\pi}{3}) & 0 \\ \sin(\frac{\pi}{3}) & \cos(\frac{\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
15 $\left\{3^{1}_{001}||2_{100}|1 0 0\right\}$ $(x + 1,-y,-z,+1,\cos(\frac{2\pi}{3}) u - \sin(\frac{2\pi}{3}) v,\sin(\frac{2\pi}{3}) u + \cos(\frac{2\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{2\pi}{3}) & -\sin(\frac{2\pi}{3}) & 0 \\ \sin(\frac{2\pi}{3}) & \cos(\frac{2\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 1 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
16 $\left\{2_{100}||-1|0 0 0\right\}$ $(-x,-y,-z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
17 $\left\{2_{001}||1|\frac{3}{2} \frac{1}{2} 0\right\}$ $(x + \frac{3}{2},y + \frac{1}{2},z,+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{3}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
18 $\left\{2_{\frac{\pi}{6}}||m_{100}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - x,y + \frac{1}{2},z,+1,\cos(\frac{\pi}{3}) u + \sin(\frac{\pi}{3}) v,\sin(\frac{\pi}{3}) u - \cos(\frac{\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{\pi}{3}) & \sin(\frac{\pi}{3}) & 0 \\ \sin(\frac{\pi}{3}) & -\cos(\frac{\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
19 $\left\{2_{001}||m_{010}|\frac{3}{2} \frac{1}{2} \frac{1}{2}\right\}$ $(x + \frac{3}{2},\frac{1}{2} - y,z + \frac{1}{2},+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{3}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
20 $\left\{2_{\frac{\pi}{6}}||2_{001}|\frac{1}{2} \frac{1}{2} \frac{1}{2}\right\}$ $(\frac{1}{2} - x,\frac{1}{2} - y,z + \frac{1}{2},+1,\cos(\frac{\pi}{3}) u + \sin(\frac{\pi}{3}) v,\sin(\frac{\pi}{3}) u - \cos(\frac{\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{\pi}{3}) & \sin(\frac{\pi}{3}) & 0 \\ \sin(\frac{\pi}{3}) & -\cos(\frac{\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
21 $\left\{2_{001}||m_{001}|\frac{3}{2} \frac{1}{2} \frac{1}{2}\right\}$ $(x + \frac{3}{2},y + \frac{1}{2},\frac{1}{2} - z,+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{3}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
22 $\left\{2_{\frac{\pi}{6}}||2_{010}|\frac{1}{2} \frac{1}{2} \frac{1}{2}\right\}$ $(\frac{1}{2} - x,y + \frac{1}{2},\frac{1}{2} - z,+1,\cos(\frac{\pi}{3}) u + \sin(\frac{\pi}{3}) v,\sin(\frac{\pi}{3}) u - \cos(\frac{\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{\pi}{3}) & \sin(\frac{\pi}{3}) & 0 \\ \sin(\frac{\pi}{3}) & -\cos(\frac{\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
23 $\left\{2_{001}||2_{100}|\frac{3}{2} \frac{1}{2} 0\right\}$ $(x + \frac{3}{2},\frac{1}{2} - y,-z,+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{3}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
24 $\left\{2_{\frac{\pi}{6}}||-1|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - x,\frac{1}{2} - y,-z,+1,\cos(\frac{\pi}{3}) u + \sin(\frac{\pi}{3}) v,\sin(\frac{\pi}{3}) u - \cos(\frac{\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{\pi}{3}) & \sin(\frac{\pi}{3}) & 0 \\ \sin(\frac{\pi}{3}) & -\cos(\frac{\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
25 $\left\{3^{2}_{001}||1|2 0 0\right\}$ $(x + 2,y,z,+1,\cos(\frac{4\pi}{3}) u - \sin(\frac{4\pi}{3}) v,\sin(\frac{4\pi}{3}) u + \cos(\frac{4\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{4\pi}{3}) & -\sin(\frac{4\pi}{3}) & 0 \\ \sin(\frac{4\pi}{3}) & \cos(\frac{4\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
26 $\left\{2_{\frac{\pi}{3}}||m_{100}|1 0 0\right\}$ $(1 - x,y,z,+1,\cos(\frac{2\pi}{3}) u + \sin(\frac{2\pi}{3}) v,\sin(\frac{2\pi}{3}) u - \cos(\frac{2\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{2\pi}{3}) & \sin(\frac{2\pi}{3}) & 0 \\ \sin(\frac{2\pi}{3}) & -\cos(\frac{2\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
27 $\left\{3^{2}_{001}||m_{010}|2 0 \frac{1}{2}\right\}$ $(x + 2,-y,z + \frac{1}{2},+1,\cos(\frac{4\pi}{3}) u - \sin(\frac{4\pi}{3}) v,\sin(\frac{4\pi}{3}) u + \cos(\frac{4\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{4\pi}{3}) & -\sin(\frac{4\pi}{3}) & 0 \\ \sin(\frac{4\pi}{3}) & \cos(\frac{4\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 2 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
28 $\left\{2_{\frac{\pi}{3}}||2_{001}|1 0 \frac{1}{2}\right\}$ $(1 - x,-y,z + \frac{1}{2},+1,\cos(\frac{2\pi}{3}) u + \sin(\frac{2\pi}{3}) v,\sin(\frac{2\pi}{3}) u - \cos(\frac{2\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{2\pi}{3}) & \sin(\frac{2\pi}{3}) & 0 \\ \sin(\frac{2\pi}{3}) & -\cos(\frac{2\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 1 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
29 $\left\{3^{2}_{001}||m_{001}|2 0 \frac{1}{2}\right\}$ $(x + 2,y,\frac{1}{2} - z,+1,\cos(\frac{4\pi}{3}) u - \sin(\frac{4\pi}{3}) v,\sin(\frac{4\pi}{3}) u + \cos(\frac{4\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{4\pi}{3}) & -\sin(\frac{4\pi}{3}) & 0 \\ \sin(\frac{4\pi}{3}) & \cos(\frac{4\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
30 $\left\{2_{\frac{\pi}{3}}||2_{010}|1 0 \frac{1}{2}\right\}$ $(1 - x,y,\frac{1}{2} - z,+1,\cos(\frac{2\pi}{3}) u + \sin(\frac{2\pi}{3}) v,\sin(\frac{2\pi}{3}) u - \cos(\frac{2\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{2\pi}{3}) & \sin(\frac{2\pi}{3}) & 0 \\ \sin(\frac{2\pi}{3}) & -\cos(\frac{2\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
31 $\left\{3^{2}_{001}||2_{100}|2 0 0\right\}$ $(x + 2,-y,-z,+1,\cos(\frac{4\pi}{3}) u - \sin(\frac{4\pi}{3}) v,\sin(\frac{4\pi}{3}) u + \cos(\frac{4\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{4\pi}{3}) & -\sin(\frac{4\pi}{3}) & 0 \\ \sin(\frac{4\pi}{3}) & \cos(\frac{4\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 2 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
32 $\left\{2_{\frac{\pi}{3}}||-1|1 0 0\right\}$ $(1 - x,-y,-z,+1,\cos(\frac{2\pi}{3}) u + \sin(\frac{2\pi}{3}) v,\sin(\frac{2\pi}{3}) u - \cos(\frac{2\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{2\pi}{3}) & \sin(\frac{2\pi}{3}) & 0 \\ \sin(\frac{2\pi}{3}) & -\cos(\frac{2\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 1 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
33 $\left\{6^{5}_{001}||1|\frac{5}{2} \frac{1}{2} 0\right\}$ $(x + \frac{5}{2},y + \frac{1}{2},z,+1,\cos(\frac{5\pi}{3}) u - \sin(\frac{5\pi}{3}) v,\sin(\frac{5\pi}{3}) u + \cos(\frac{5\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{5\pi}{3}) & -\sin(\frac{5\pi}{3}) & 0 \\ \sin(\frac{5\pi}{3}) & \cos(\frac{5\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{5}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
34 $\left\{2_{010}||m_{100}|\frac{3}{2} \frac{1}{2} 0\right\}$ $(\frac{3}{2} - x,y + \frac{1}{2},z,+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
35 $\left\{6^{5}_{001}||m_{010}|\frac{5}{2} \frac{1}{2} \frac{1}{2}\right\}$ $(x + \frac{5}{2},\frac{1}{2} - y,z + \frac{1}{2},+1,\cos(\frac{5\pi}{3}) u - \sin(\frac{5\pi}{3}) v,\sin(\frac{5\pi}{3}) u + \cos(\frac{5\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{5\pi}{3}) & -\sin(\frac{5\pi}{3}) & 0 \\ \sin(\frac{5\pi}{3}) & \cos(\frac{5\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{5}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
36 $\left\{2_{010}||2_{001}|\frac{3}{2} \frac{1}{2} \frac{1}{2}\right\}$ $(\frac{3}{2} - x,\frac{1}{2} - y,z + \frac{1}{2},+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
37 $\left\{6^{5}_{001}||m_{001}|\frac{5}{2} \frac{1}{2} \frac{1}{2}\right\}$ $(x + \frac{5}{2},y + \frac{1}{2},\frac{1}{2} - z,+1,\cos(\frac{5\pi}{3}) u - \sin(\frac{5\pi}{3}) v,\sin(\frac{5\pi}{3}) u + \cos(\frac{5\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{5\pi}{3}) & -\sin(\frac{5\pi}{3}) & 0 \\ \sin(\frac{5\pi}{3}) & \cos(\frac{5\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{5}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
38 $\left\{2_{010}||2_{010}|\frac{3}{2} \frac{1}{2} \frac{1}{2}\right\}$ $(\frac{3}{2} - x,y + \frac{1}{2},\frac{1}{2} - z,+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
39 $\left\{6^{5}_{001}||2_{100}|\frac{5}{2} \frac{1}{2} 0\right\}$ $(x + \frac{5}{2},\frac{1}{2} - y,-z,+1,\cos(\frac{5\pi}{3}) u - \sin(\frac{5\pi}{3}) v,\sin(\frac{5\pi}{3}) u + \cos(\frac{5\pi}{3}) v,w)$ $$\begin{bmatrix}\cos(\frac{5\pi}{3}) & -\sin(\frac{5\pi}{3}) & 0 \\ \sin(\frac{5\pi}{3}) & \cos(\frac{5\pi}{3}) & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{5}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
40 $\left\{2_{010}||-1|\frac{3}{2} \frac{1}{2} 0\right\}$ $(\frac{3}{2} - x,\frac{1}{2} - y,-z,+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
41 $\left\{2_{\frac{2\pi}{3}}||m_{100}|2 0 0\right\}$ $(2 - x,y,z,+1,\cos(\frac{4\pi}{3}) u + \sin(\frac{4\pi}{3}) v,\sin(\frac{4\pi}{3}) u - \cos(\frac{4\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{4\pi}{3}) & \sin(\frac{4\pi}{3}) & 0 \\ \sin(\frac{4\pi}{3}) & -\cos(\frac{4\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
42 $\left\{2_{\frac{2\pi}{3}}||2_{001}|2 0 \frac{1}{2}\right\}$ $(2 - x,-y,z + \frac{1}{2},+1,\cos(\frac{4\pi}{3}) u + \sin(\frac{4\pi}{3}) v,\sin(\frac{4\pi}{3}) u - \cos(\frac{4\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{4\pi}{3}) & \sin(\frac{4\pi}{3}) & 0 \\ \sin(\frac{4\pi}{3}) & -\cos(\frac{4\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 2 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
43 $\left\{2_{\frac{2\pi}{3}}||2_{010}|2 0 \frac{1}{2}\right\}$ $(2 - x,y,\frac{1}{2} - z,+1,\cos(\frac{4\pi}{3}) u + \sin(\frac{4\pi}{3}) v,\sin(\frac{4\pi}{3}) u - \cos(\frac{4\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{4\pi}{3}) & \sin(\frac{4\pi}{3}) & 0 \\ \sin(\frac{4\pi}{3}) & -\cos(\frac{4\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
44 $\left\{2_{\frac{2\pi}{3}}||-1|2 0 0\right\}$ $(2 - x,-y,-z,+1,\cos(\frac{4\pi}{3}) u + \sin(\frac{4\pi}{3}) v,\sin(\frac{4\pi}{3}) u - \cos(\frac{4\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{4\pi}{3}) & \sin(\frac{4\pi}{3}) & 0 \\ \sin(\frac{4\pi}{3}) & -\cos(\frac{4\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 2 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
45 $\left\{2_{\frac{5\pi}{6}}||m_{100}|\frac{5}{2} \frac{1}{2} 0\right\}$ $(\frac{5}{2} - x,y + \frac{1}{2},z,+1,\cos(\frac{5\pi}{3}) u + \sin(\frac{5\pi}{3}) v,\sin(\frac{5\pi}{3}) u - \cos(\frac{5\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{5\pi}{3}) & \sin(\frac{5\pi}{3}) & 0 \\ \sin(\frac{5\pi}{3}) & -\cos(\frac{5\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{5}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
46 $\left\{2_{\frac{5\pi}{6}}||2_{001}|\frac{5}{2} \frac{1}{2} \frac{1}{2}\right\}$ $(\frac{5}{2} - x,\frac{1}{2} - y,z + \frac{1}{2},+1,\cos(\frac{5\pi}{3}) u + \sin(\frac{5\pi}{3}) v,\sin(\frac{5\pi}{3}) u - \cos(\frac{5\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{5\pi}{3}) & \sin(\frac{5\pi}{3}) & 0 \\ \sin(\frac{5\pi}{3}) & -\cos(\frac{5\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{5}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
47 $\left\{2_{\frac{5\pi}{6}}||2_{010}|\frac{5}{2} \frac{1}{2} \frac{1}{2}\right\}$ $(\frac{5}{2} - x,y + \frac{1}{2},\frac{1}{2} - z,+1,\cos(\frac{5\pi}{3}) u + \sin(\frac{5\pi}{3}) v,\sin(\frac{5\pi}{3}) u - \cos(\frac{5\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{5\pi}{3}) & \sin(\frac{5\pi}{3}) & 0 \\ \sin(\frac{5\pi}{3}) & -\cos(\frac{5\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{5}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
48 $\left\{2_{\frac{5\pi}{6}}||-1|\frac{5}{2} \frac{1}{2} 0\right\}$ $(\frac{5}{2} - x,\frac{1}{2} - y,-z,+1,\cos(\frac{5\pi}{3}) u + \sin(\frac{5\pi}{3}) v,\sin(\frac{5\pi}{3}) u - \cos(\frac{5\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{5\pi}{3}) & \sin(\frac{5\pi}{3}) & 0 \\ \sin(\frac{5\pi}{3}) & -\cos(\frac{5\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{5}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{m_{001}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,u,v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
wyckoff position site symmetry Coordinates
$(0,0,0\mid mx,my,mz)+(\frac{1}{2},\frac{1}{2},0\mid mx/2 - \sqrt{3} my/2,\sqrt{3} mx/2 + my/2,mz)+(1,0,0\mid -mx/2 - \sqrt{3} my/2,\sqrt{3} mx/2 - my/2,mz)+(\frac{3}{2},\frac{1}{2},0\mid -mx,-my,mz)+(2,0,0\mid -mx/2 + \sqrt{3} my/2,-\sqrt{3} mx/2 - my/2,mz)+(\frac{5}{2},\frac{1}{2},0\mid mx/2 + \sqrt{3} my/2,-\sqrt{3} mx/2 + my/2,mz)$
48h $(x,y,z\mid mx,my,0),(-x,-y,z + \frac{1}{2}\mid mx,-my,0),(-x,y,\frac{1}{2} - z\mid mx,-my,0),(x,-y,-z\mid mx,my,0),(-x,-y,-z\mid mx,-my,0),(x,y,\frac{1}{2} - z\mid mx,my,0),(x,-y,z + \frac{1}{2}\mid mx,my,0),(-x,y,z\mid mx,-my,0)$
24g $(x,y,\frac{1}{4}\mid mx,my,0),(-x,-y,\frac{3}{4}\mid mx,-my,0),(-x,y,\frac{1}{4}\mid mx,-my,0),(x,-y,\frac{3}{4}\mid mx,my,0)$
24f $(0,y,z\mid mx,0,0),(0,-y,z + \frac{1}{2}\mid mx,0,0),(0,y,\frac{1}{2} - z\mid mx,0,0),(0,-y,-z\mid mx,0,0)$
24e $(x,0,0\mid mx,my,0),(-x,0,\frac{1}{2}\mid mx,-my,0),(-x,0,0\mid mx,-my,0),(x,0,\frac{1}{2}\mid mx,my,0)$
24d $(\frac{1}{4},\frac{1}{4},0\mid \sqrt{3} mx/2,mx/2,0),(\frac{3}{4},\frac{3}{4},\frac{1}{2}\mid 0,mx,0),(\frac{3}{4},\frac{1}{4},\frac{1}{2}\mid 0,mx,0),(\frac{1}{4},\frac{3}{4},0\mid \sqrt{3} mx/2,mx/2,0)$
12c $(0,y,\frac{1}{4}\mid mx,0,0),(0,-y,\frac{3}{4}\mid mx,0,0)$
12b $(0,\frac{1}{2},0\mid mx,0,0),(0,\frac{1}{2},\frac{1}{2}\mid mx,0,0)$
12a $(0,0,0\mid mx,0,0),(0,0,\frac{1}{2}\mid mx,0,0)$
Site symmetry: $^{1}1^{m}1$
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 $\left\{\ce{^{m_{001}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,u,v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $..^{1}m^{m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
3 $\left\{1||m_{001}|0 0 \frac{1}{2}\right\}$ $(x,y,\frac{1}{2} - z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{m_{001}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,u,v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $^{2_{100}}m..^{m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
6 $\left\{2_{100}||m_{100}|0 0 0\right\}$ $(-x,y,z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{m_{001}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,u,v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $^{1}2..^{m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
7 $\left\{1||2_{100}|0 0 0\right\}$ $(x,-y,-z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{m_{001}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,u,v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $^{2_{\frac{\pi}{6}}}\!-\!1^{m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
24 $\left\{2_{\frac{\pi}{6}}||-1|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - x,\frac{1}{2} - y,-z,+1,\cos(\frac{\pi}{3}) u + \sin(\frac{\pi}{3}) v,\sin(\frac{\pi}{3}) u - \cos(\frac{\pi}{3}) v,-w)$ $$\begin{bmatrix}\cos(\frac{\pi}{3}) & \sin(\frac{\pi}{3}) & 0 \\ \sin(\frac{\pi}{3}) & -\cos(\frac{\pi}{3}) & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{m_{001}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,u,v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $^{2_{100}}m^{2_{100}}2^{1}m^{m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
3 $\left\{1||m_{001}|0 0 \frac{1}{2}\right\}$ $(x,y,\frac{1}{2} - z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
6 $\left\{2_{100}||m_{100}|0 0 0\right\}$ $(-x,y,z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
13 $\left\{2_{100}||2_{010}|0 0 \frac{1}{2}\right\}$ $(-x,y,\frac{1}{2} - z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{m_{001}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,u,v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $^{1}2/^{2_{100}}m..^{m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
6 $\left\{2_{100}||m_{100}|0 0 0\right\}$ $(-x,y,z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
7 $\left\{1||2_{100}|0 0 0\right\}$ $(x,-y,-z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
16 $\left\{2_{100}||-1|0 0 0\right\}$ $(-x,-y,-z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{m_{001}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,u,v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $^{1}2/^{2_{100}}m..^{m}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
6 $\left\{2_{100}||m_{100}|0 0 0\right\}$ $(-x,y,z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
7 $\left\{1||2_{100}|0 0 0\right\}$ $(x,-y,-z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
16 $\left\{2_{100}||-1|0 0 0\right\}$ $(-x,-y,-z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
extra__U_E_0(without_identity)
op_index Seitz coordinate spin_expr space_expr
1 $\left\{\ce{^{m_{001}}{1}}||1|0 0 0\right\}$ $(x,y,z,-1,u,v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$