227.2.1.2
Spin space group detail page with configuration, notation, nontrivial spin-space point group, spin-space point group, symmetry operations, and spin Wyckoff-position data.
Metadata
Configuration: Non-coplanar
Type: type-t
G0 / L0: 227 / 2
Identifier: 227.2.1.2
it / ik: 24 / 1
Nontrivial spin-space point group: $-43m$
Spin-space point group: $\!-\!43m$
International Notation: $$F\ce{^{2_{010}}{d}}\ce{^{3^{2}_{\text{-}11\text{-}1}}{\text{-}3}}\ce{^{m_{1\text{-}10}}{m}}$$
Conventional to Primitive Matrix P:
$$\begin{bmatrix}0 & \frac{1}{2} & \frac{1}{2} \\ \frac{1}{2} & 0 & \frac{1}{2} \\ \frac{1}{2} & \frac{1}{2} & 0\end{bmatrix}$$
Note: (aC, bC, cC) P = (aP, bP, cP)
Transformation Matrix M:
$$\left[\begin{array}{ccc|c}-\frac{1}{2} & 0 & \frac{1}{2} & \frac{1}{2} \\ 0 & \frac{1}{2} & -\frac{1}{2} & \frac{1}{4} \\ -\frac{1}{2} & -\frac{1}{2} & 0 & \frac{1}{4}\end{array}\right]$$
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 227.2.1.2, 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 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
2 $\left\{1||1|\frac{1}{2} \frac{1}{2} 0\right\}$ $(x + \frac{1}{2},y + \frac{1}{2},z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
3 $\left\{1||1|\frac{1}{2} 0 \frac{1}{2}\right\}$ $(x + \frac{1}{2},y,z + \frac{1}{2},+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
4 $\left\{1||1|0 \frac{1}{2} \frac{1}{2}\right\}$ $(x,y + \frac{1}{2},z + \frac{1}{2},+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
U_E_0
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
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 $\left\{2_{010}||m_{100}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(\frac{1}{2} - x,y + \frac{1}{4},z + \frac{3}{4},+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{3}{4}\end{array}\right]$$
3 $\left\{3^{2}_{-11-1}||-3^{1}_{111}|0 0 0\right\}$ $(-z,-x,-y,+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0\end{array}\right]$$
4 $\left\{m_{1-10}||m_{110}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(\frac{1}{4} - y,\frac{3}{4} - x,z + \frac{1}{2},-1,v,u,w)$ $$\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
5 $\left\{3^{2}_{-1-11}||3^{1}_{-11-1}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(z + \frac{1}{2},\frac{1}{4} - x,\frac{3}{4} - y,+1,v,-w,-u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & -1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{3}{4}\end{array}\right]$$
6 $\left\{-4^{3}_{001}||4^{3}_{001}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(y + \frac{1}{4},-x,z + \frac{1}{4},-1,-v,u,-w)$ $$\begin{bmatrix}0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{4} \\ -1 & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{4}\end{array}\right]$$
7 $\left\{3^{2}_{1-1-1}||3^{1}_{-1-11}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(\frac{1}{4} - z,x + \frac{1}{2},\frac{3}{4} - y,+1,-v,w,-u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & 1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{3}{4}\end{array}\right]$$
8 $\left\{3^{1}_{-11-1}||3^{2}_{111}|0 0 0\right\}$ $(y,z,x,+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$
9 $\left\{-4^{3}_{100}||4^{3}_{010}|\frac{1}{2} \frac{3}{4} \frac{1}{4}\right\}$ $(\frac{1}{2} - z,y + \frac{3}{4},x + \frac{1}{4},-1,-u,-w,v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{3}{4} \\ 1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
10 $\left\{3^{1}_{111}||-3^{2}_{1-1-1}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(y + \frac{1}{4},\frac{1}{2} - z,x + \frac{3}{4},+1,w,u,v)$ $$\begin{bmatrix}0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
11 $\left\{-4^{1}_{100}||-4^{1}_{010}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(\frac{3}{4} - z,\frac{3}{4} - y,x,-1,-u,w,-v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{3}{4} \\ 1 & 0 & 0 & 0\end{array}\right]$$
12 $\left\{3^{1}_{-1-11}||-3^{2}_{-11-1}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(y + \frac{1}{4},z + \frac{3}{4},\frac{1}{2} - x,+1,-w,u,-v)$ $$\begin{bmatrix}0 & 0 & -1 \\ 1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
13 $\left\{1||-1|0 0 0\right\}$ $(-x,-y,-z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
14 $\left\{-4^{3}_{010}||-4^{1}_{100}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(\frac{3}{4} - x,z + \frac{1}{2},\frac{1}{4} - y,-1,w,-v,-u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{4}\end{array}\right]$$
15 $\left\{2_{001}||2_{001}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(\frac{1}{4} - x,\frac{3}{4} - y,z + \frac{1}{2},+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
16 $\left\{m_{101}||2_{011}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(-x,z + \frac{1}{4},y + \frac{1}{4},-1,-w,v,-u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & 1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{4} \\ 0 & 1 & 0 & \frac{1}{4}\end{array}\right]$$
17 $\left\{2_{010}||2_{100}|\frac{1}{2} \frac{3}{4} \frac{1}{4}\right\}$ $(x + \frac{1}{2},\frac{3}{4} - y,\frac{1}{4} - z,+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{1}{4}\end{array}\right]$$
18 $\left\{3^{2}_{-11-1}||3^{1}_{111}|0 0 0\right\}$ $(z,x,y,+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0\end{array}\right]$$
19 $\left\{m_{1-10}||2_{110}|\frac{3}{4} \frac{1}{4} \frac{1}{2}\right\}$ $(y + \frac{3}{4},x + \frac{1}{4},\frac{1}{2} - z,-1,v,u,w)$ $$\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{3}{4} \\ 1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
20 $\left\{3^{2}_{-1-11}||-3^{1}_{-11-1}|\frac{1}{2} \frac{3}{4} \frac{1}{4}\right\}$ $(\frac{1}{2} - z,x + \frac{3}{4},y + \frac{1}{4},+1,v,-w,-u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & -1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{3}{4} \\ 0 & 1 & 0 & \frac{1}{4}\end{array}\right]$$
21 $\left\{-4^{3}_{001}||-4^{3}_{001}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(\frac{3}{4} - y,x,\frac{3}{4} - z,-1,-v,u,-w)$ $$\begin{bmatrix}0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{3}{4} \\ 1 & 0 & 0 & 0 \\ 0 & 0 & -1 & \frac{3}{4}\end{array}\right]$$
22 $\left\{3^{2}_{1-1-1}||-3^{1}_{-1-11}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(z + \frac{3}{4},\frac{1}{2} - x,y + \frac{1}{4},+1,-v,w,-u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & 1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{4}\end{array}\right]$$
23 $\left\{3^{1}_{-11-1}||-3^{2}_{111}|0 0 0\right\}$ $(-y,-z,-x,+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ -1 & 0 & 0 & 0\end{array}\right]$$
24 $\left\{-4^{3}_{100}||-4^{3}_{010}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(z + \frac{1}{2},\frac{1}{4} - y,\frac{3}{4} - x,-1,-u,-w,v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
25 $\left\{3^{1}_{111}||3^{2}_{1-1-1}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(\frac{3}{4} - y,z + \frac{1}{2},\frac{1}{4} - x,+1,w,u,v)$ $$\begin{bmatrix}0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
26 $\left\{-4^{1}_{100}||4^{1}_{010}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(z + \frac{1}{4},y + \frac{1}{4},-x,-1,-u,w,-v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{4} \\ 0 & 1 & 0 & \frac{1}{4} \\ -1 & 0 & 0 & 0\end{array}\right]$$
27 $\left\{3^{1}_{-1-11}||3^{2}_{-11-1}|\frac{3}{4} \frac{1}{4} \frac{1}{2}\right\}$ $(\frac{3}{4} - y,\frac{1}{4} - z,x + \frac{1}{2},+1,-w,u,-v)$ $$\begin{bmatrix}0 & 0 & -1 \\ 1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
28 $\left\{-4^{3}_{010}||4^{1}_{100}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(x + \frac{1}{4},\frac{1}{2} - z,y + \frac{3}{4},-1,w,-v,-u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{3}{4}\end{array}\right]$$
29 $\left\{2_{001}||m_{001}|\frac{3}{4} \frac{1}{4} \frac{1}{2}\right\}$ $(x + \frac{3}{4},y + \frac{1}{4},\frac{1}{2} - z,+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{3}{4} \\ 0 & 1 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
30 $\left\{m_{101}||m_{011}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(x,\frac{3}{4} - z,\frac{3}{4} - y,-1,-w,v,-u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & 1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 0 & -1 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{3}{4}\end{array}\right]$$
31 $\left\{-4^{1}_{001}||4^{1}_{001}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(-y,x + \frac{1}{4},z + \frac{1}{4},-1,v,-u,-w)$ $$\begin{bmatrix}0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ 1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{1}{4}\end{array}\right]$$
32 $\left\{-4^{1}_{010}||4^{3}_{100}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(x + \frac{1}{4},z + \frac{3}{4},\frac{1}{2} - y,-1,-w,-v,u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & -1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{1}{2}\end{array}\right]$$
33 $\left\{2_{100}||m_{010}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(x + \frac{1}{4},\frac{1}{2} - y,z + \frac{3}{4},+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{3}{4}\end{array}\right]$$
34 $\left\{3^{1}_{1-1-1}||-3^{2}_{-1-11}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(\frac{1}{2} - y,z + \frac{1}{4},x + \frac{3}{4},+1,-w,-u,v)$ $$\begin{bmatrix}0 & 0 & -1 \\ -1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
35 $\left\{m_{01-1}||2_{101}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(z + \frac{3}{4},\frac{1}{2} - y,x + \frac{1}{4},-1,u,w,v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
36 $\left\{m_{011}||2_{-101}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - z,\frac{1}{2} - y,-x,-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & 0\end{array}\right]$$
37 $\left\{m_{110}||m_{1-10}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(y + \frac{1}{2},x + \frac{1}{2},z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
38 $\left\{-4^{1}_{001}||-4^{1}_{001}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(y + \frac{1}{2},\frac{1}{4} - x,\frac{3}{4} - z,-1,v,-u,-w)$ $$\begin{bmatrix}0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{3}{4}\end{array}\right]$$
39 $\left\{-4^{1}_{010}||-4^{3}_{100}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(\frac{1}{4} - x,\frac{3}{4} - z,y + \frac{1}{2},-1,-w,-v,u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & -1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{3}{4} \\ 0 & 1 & 0 & \frac{1}{2}\end{array}\right]$$
40 $\left\{2_{100}||2_{010}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(\frac{1}{4} - x,y,\frac{1}{4} - z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{4} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{4}\end{array}\right]$$
41 $\left\{3^{1}_{1-1-1}||3^{2}_{-1-11}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(y,\frac{1}{4} - z,\frac{1}{4} - x,+1,-w,-u,v)$ $$\begin{bmatrix}0 & 0 & -1 \\ -1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
42 $\left\{m_{01-1}||m_{101}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(\frac{3}{4} - z,y,\frac{3}{4} - x,-1,u,w,v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{3}{4} \\ 0 & 1 & 0 & 0 \\ -1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
43 $\left\{m_{011}||m_{-101}|0 0 0\right\}$ $(z,y,x,-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$
44 $\left\{m_{110}||2_{1-10}|0 0 0\right\}$ $(-y,-x,-z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
45 $\left\{3^{2}_{111}||-3^{1}_{1-1-1}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(z + \frac{1}{4},x + \frac{3}{4},\frac{1}{2} - y,+1,v,w,u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{1}{2}\end{array}\right]$$
46 $\left\{m_{-101}||m_{01-1}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(x + \frac{1}{2},z + \frac{1}{2},y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{2} \\ 0 & 1 & 0 & 0\end{array}\right]$$
47 $\left\{3^{2}_{111}||3^{1}_{1-1-1}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(\frac{3}{4} - z,\frac{3}{4} - x,y,+1,v,w,u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{3}{4} \\ 0 & 1 & 0 & 0\end{array}\right]$$
48 $\left\{m_{-101}||2_{01-1}|\frac{1}{2} 0 \frac{1}{2}\right\}$ $(\frac{1}{2} - x,-z,\frac{1}{2} - y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0 \\ 0 & -1 & 0 & \frac{1}{2}\end{array}\right]$$
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 $\left\{2_{010}||m_{100}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(\frac{1}{2} - x,y + \frac{1}{4},z + \frac{3}{4},+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{3}{4}\end{array}\right]$$
3 $\left\{3^{2}_{-11-1}||-3^{1}_{111}|0 0 0\right\}$ $(-z,-x,-y,+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0\end{array}\right]$$
4 $\left\{m_{1-10}||m_{110}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(\frac{1}{4} - y,\frac{3}{4} - x,z + \frac{1}{2},-1,v,u,w)$ $$\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
5 $\left\{1||1|\frac{1}{2} \frac{1}{2} 0\right\}$ $(x + \frac{1}{2},y + \frac{1}{2},z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
6 $\left\{1||1|\frac{1}{2} 0 \frac{1}{2}\right\}$ $(x + \frac{1}{2},y,z + \frac{1}{2},+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
7 $\left\{1||1|0 \frac{1}{2} \frac{1}{2}\right\}$ $(x,y + \frac{1}{2},z + \frac{1}{2},+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
8 $\left\{3^{2}_{-1-11}||3^{1}_{-11-1}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(z + \frac{1}{2},\frac{1}{4} - x,\frac{3}{4} - y,+1,v,-w,-u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & -1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{3}{4}\end{array}\right]$$
9 $\left\{-4^{3}_{001}||4^{3}_{001}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(y + \frac{1}{4},-x,z + \frac{1}{4},-1,-v,u,-w)$ $$\begin{bmatrix}0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{4} \\ -1 & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{4}\end{array}\right]$$
10 $\left\{2_{010}||m_{100}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(-x,y + \frac{3}{4},z + \frac{3}{4},+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{3}{4}\end{array}\right]$$
11 $\left\{2_{010}||m_{100}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(-x,y + \frac{1}{4},z + \frac{1}{4},+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{1}{4}\end{array}\right]$$
12 $\left\{2_{010}||m_{100}|\frac{1}{2} \frac{3}{4} \frac{1}{4}\right\}$ $(\frac{1}{2} - x,y + \frac{3}{4},z + \frac{1}{4},+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{1}{4}\end{array}\right]$$
13 $\left\{3^{2}_{-11-1}||-3^{1}_{111}|0 \frac{1}{2} \frac{1}{2}\right\}$ $(-z,\frac{1}{2} - x,\frac{1}{2} - y,+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & 0 \\ -1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2}\end{array}\right]$$
14 $\left\{m_{1-10}||m_{110}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(\frac{1}{4} - y,\frac{1}{4} - x,z,-1,v,u,w)$ $$\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & 0\end{array}\right]$$
15 $\left\{3^{2}_{-1-11}||3^{1}_{-11-1}|\frac{1}{2} \frac{3}{4} \frac{1}{4}\right\}$ $(z + \frac{1}{2},\frac{3}{4} - x,\frac{1}{4} - y,+1,v,-w,-u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & -1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{1}{4}\end{array}\right]$$
16 $\left\{-4^{3}_{001}||4^{3}_{001}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(y + \frac{1}{4},\frac{1}{2} - x,z + \frac{3}{4},-1,-v,u,-w)$ $$\begin{bmatrix}0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{3}{4}\end{array}\right]$$
17 $\left\{3^{2}_{1-1-1}||3^{1}_{-1-11}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(\frac{1}{4} - z,x + \frac{1}{2},\frac{3}{4} - y,+1,-v,w,-u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & 1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{3}{4}\end{array}\right]$$
18 $\left\{3^{1}_{-11-1}||3^{2}_{111}|0 0 0\right\}$ $(y,z,x,+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$
19 $\left\{-4^{3}_{100}||4^{3}_{010}|\frac{1}{2} \frac{3}{4} \frac{1}{4}\right\}$ $(\frac{1}{2} - z,y + \frac{3}{4},x + \frac{1}{4},-1,-u,-w,v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{3}{4} \\ 1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
20 $\left\{3^{2}_{-11-1}||-3^{1}_{111}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - z,\frac{1}{2} - x,-y,+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & 0\end{array}\right]$$
21 $\left\{3^{2}_{-11-1}||-3^{1}_{111}|\frac{1}{2} 0 \frac{1}{2}\right\}$ $(\frac{1}{2} - z,-x,\frac{1}{2} - y,+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{2} \\ -1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{1}{2}\end{array}\right]$$
22 $\left\{3^{1}_{111}||-3^{2}_{1-1-1}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(y + \frac{1}{4},\frac{1}{2} - z,x + \frac{3}{4},+1,w,u,v)$ $$\begin{bmatrix}0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
23 $\left\{-4^{1}_{100}||-4^{1}_{010}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(\frac{3}{4} - z,\frac{3}{4} - y,x,-1,-u,w,-v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{3}{4} \\ 1 & 0 & 0 & 0\end{array}\right]$$
24 $\left\{3^{2}_{1-1-1}||3^{1}_{-1-11}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(\frac{1}{4} - z,x,\frac{1}{4} - y,+1,-v,w,-u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & 1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{4} \\ 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{1}{4}\end{array}\right]$$
25 $\left\{3^{2}_{1-1-1}||3^{1}_{-1-11}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(\frac{3}{4} - z,x,\frac{3}{4} - y,+1,-v,w,-u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & 1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{3}{4} \\ 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{3}{4}\end{array}\right]$$
26 $\left\{3^{2}_{1-1-1}||3^{1}_{-1-11}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(\frac{3}{4} - z,x + \frac{1}{2},\frac{1}{4} - y,+1,-v,w,-u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & 1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{3}{4} \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{4}\end{array}\right]$$
27 $\left\{3^{1}_{-11-1}||3^{2}_{111}|\frac{1}{2} 0 \frac{1}{2}\right\}$ $(y + \frac{1}{2},z,x + \frac{1}{2},+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
28 $\left\{-4^{3}_{100}||4^{3}_{010}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(-z,y + \frac{3}{4},x + \frac{3}{4},-1,-u,-w,v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & 0 \\ 0 & 1 & 0 & \frac{3}{4} \\ 1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
29 $\left\{3^{1}_{111}||-3^{2}_{1-1-1}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(y + \frac{3}{4},\frac{1}{2} - z,x + \frac{1}{4},+1,w,u,v)$ $$\begin{bmatrix}0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
30 $\left\{-4^{1}_{100}||-4^{1}_{010}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(\frac{1}{4} - z,\frac{3}{4} - y,x + \frac{1}{2},-1,-u,w,-v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{3}{4} \\ 1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
31 $\left\{3^{1}_{-1-11}||-3^{2}_{-11-1}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(y + \frac{1}{4},z + \frac{3}{4},\frac{1}{2} - x,+1,-w,u,-v)$ $$\begin{bmatrix}0 & 0 & -1 \\ 1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
32 $\left\{1||-1|0 0 0\right\}$ $(-x,-y,-z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
33 $\left\{-4^{3}_{010}||-4^{1}_{100}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(\frac{3}{4} - x,z + \frac{1}{2},\frac{1}{4} - y,-1,w,-v,-u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{4}\end{array}\right]$$
34 $\left\{3^{1}_{-11-1}||3^{2}_{111}|0 \frac{1}{2} \frac{1}{2}\right\}$ $(y,z + \frac{1}{2},x + \frac{1}{2},+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
35 $\left\{3^{1}_{-11-1}||3^{2}_{111}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(y + \frac{1}{2},z + \frac{1}{2},x,+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{2} \\ 1 & 0 & 0 & 0\end{array}\right]$$
36 $\left\{2_{001}||2_{001}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(\frac{1}{4} - x,\frac{3}{4} - y,z + \frac{1}{2},+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
37 $\left\{m_{101}||2_{011}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(-x,z + \frac{1}{4},y + \frac{1}{4},-1,-w,v,-u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & 1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{4} \\ 0 & 1 & 0 & \frac{1}{4}\end{array}\right]$$
38 $\left\{3^{1}_{-1-11}||-3^{2}_{-11-1}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(y + \frac{3}{4},z + \frac{3}{4},-x,+1,-w,u,-v)$ $$\begin{bmatrix}0 & 0 & -1 \\ 1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{3}{4} \\ -1 & 0 & 0 & 0\end{array}\right]$$
39 $\left\{3^{1}_{-1-11}||-3^{2}_{-11-1}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(y + \frac{1}{4},z + \frac{1}{4},-x,+1,-w,u,-v)$ $$\begin{bmatrix}0 & 0 & -1 \\ 1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{1}{4} \\ -1 & 0 & 0 & 0\end{array}\right]$$
40 $\left\{3^{1}_{-1-11}||-3^{2}_{-11-1}|\frac{3}{4} \frac{1}{4} \frac{1}{2}\right\}$ $(y + \frac{3}{4},z + \frac{1}{4},\frac{1}{2} - x,+1,-w,u,-v)$ $$\begin{bmatrix}0 & 0 & -1 \\ 1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
41 $\left\{1||-1|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - x,\frac{1}{2} - y,-z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
42 $\left\{-4^{3}_{010}||-4^{1}_{100}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(\frac{1}{4} - x,z,\frac{1}{4} - y,-1,w,-v,-u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & 0 \\ 0 & -1 & 0 & \frac{1}{4}\end{array}\right]$$
43 $\left\{2_{001}||2_{001}|\frac{3}{4} \frac{1}{4} \frac{1}{2}\right\}$ $(\frac{3}{4} - x,\frac{1}{4} - y,z + \frac{1}{2},+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
44 $\left\{m_{101}||2_{011}|\frac{1}{2} \frac{3}{4} \frac{1}{4}\right\}$ $(\frac{1}{2} - x,z + \frac{3}{4},y + \frac{1}{4},-1,-w,v,-u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & 1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{3}{4} \\ 0 & 1 & 0 & \frac{1}{4}\end{array}\right]$$
45 $\left\{1||-1|\frac{1}{2} 0 \frac{1}{2}\right\}$ $(\frac{1}{2} - x,-y,\frac{1}{2} - z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
46 $\left\{m_{1-10}||2_{110}|\frac{3}{4} \frac{1}{4} \frac{1}{2}\right\}$ $(y + \frac{3}{4},x + \frac{1}{4},\frac{1}{2} - z,-1,v,u,w)$ $$\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{3}{4} \\ 1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
47 $\left\{1||-1|0 \frac{1}{2} \frac{1}{2}\right\}$ $(-x,\frac{1}{2} - y,\frac{1}{2} - z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
48 $\left\{3^{2}_{-1-11}||-3^{1}_{-11-1}|\frac{1}{2} \frac{3}{4} \frac{1}{4}\right\}$ $(\frac{1}{2} - z,x + \frac{3}{4},y + \frac{1}{4},+1,v,-w,-u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & -1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{3}{4} \\ 0 & 1 & 0 & \frac{1}{4}\end{array}\right]$$
49 $\left\{-4^{3}_{001}||-4^{3}_{001}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(\frac{3}{4} - y,x,\frac{3}{4} - z,-1,-v,u,-w)$ $$\begin{bmatrix}0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{3}{4} \\ 1 & 0 & 0 & 0 \\ 0 & 0 & -1 & \frac{3}{4}\end{array}\right]$$
50 $\left\{2_{010}||2_{100}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(x,\frac{1}{4} - y,\frac{1}{4} - z,+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{4}\end{array}\right]$$
51 $\left\{2_{010}||2_{100}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(x,\frac{3}{4} - y,\frac{3}{4} - z,+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{3}{4}\end{array}\right]$$
52 $\left\{2_{010}||2_{100}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(x + \frac{1}{2},\frac{1}{4} - y,\frac{3}{4} - z,+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{3}{4}\end{array}\right]$$
53 $\left\{3^{2}_{-11-1}||3^{1}_{111}|0 \frac{1}{2} \frac{1}{2}\right\}$ $(z,x + \frac{1}{2},y + \frac{1}{2},+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{2}\end{array}\right]$$
54 $\left\{m_{1-10}||2_{110}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(y + \frac{3}{4},x + \frac{3}{4},-z,-1,v,u,w)$ $$\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{3}{4} \\ 1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & 0\end{array}\right]$$
55 $\left\{3^{2}_{-1-11}||-3^{1}_{-11-1}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(\frac{1}{2} - z,x + \frac{1}{4},y + \frac{3}{4},+1,v,-w,-u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & -1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{1}{4} \\ 0 & 1 & 0 & \frac{3}{4}\end{array}\right]$$
56 $\left\{-4^{3}_{001}||-4^{3}_{001}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(\frac{3}{4} - y,x + \frac{1}{2},\frac{1}{4} - z,-1,-v,u,-w)$ $$\begin{bmatrix}0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{3}{4} \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{1}{4}\end{array}\right]$$
57 $\left\{2_{010}||2_{100}|\frac{1}{2} \frac{3}{4} \frac{1}{4}\right\}$ $(x + \frac{1}{2},\frac{3}{4} - y,\frac{1}{4} - z,+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{1}{4}\end{array}\right]$$
58 $\left\{3^{2}_{-11-1}||3^{1}_{111}|0 0 0\right\}$ $(z,x,y,+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0\end{array}\right]$$
59 $\left\{3^{2}_{-11-1}||3^{1}_{111}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(z + \frac{1}{2},x + \frac{1}{2},y,+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & 0\end{array}\right]$$
60 $\left\{-4^{3}_{100}||-4^{3}_{010}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(z + \frac{1}{2},\frac{1}{4} - y,\frac{3}{4} - x,-1,-u,-w,v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
61 $\left\{3^{2}_{-11-1}||3^{1}_{111}|\frac{1}{2} 0 \frac{1}{2}\right\}$ $(z + \frac{1}{2},x,y + \frac{1}{2},+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{2} \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & \frac{1}{2}\end{array}\right]$$
62 $\left\{3^{1}_{111}||3^{2}_{1-1-1}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(\frac{3}{4} - y,z + \frac{1}{2},\frac{1}{4} - x,+1,w,u,v)$ $$\begin{bmatrix}0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
63 $\left\{-4^{1}_{100}||4^{1}_{010}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(z + \frac{1}{4},y + \frac{1}{4},-x,-1,-u,w,-v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{4} \\ 0 & 1 & 0 & \frac{1}{4} \\ -1 & 0 & 0 & 0\end{array}\right]$$
64 $\left\{3^{2}_{1-1-1}||-3^{1}_{-1-11}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(z + \frac{3}{4},-x,y + \frac{3}{4},+1,-v,w,-u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & 1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{3}{4} \\ -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & \frac{3}{4}\end{array}\right]$$
65 $\left\{3^{2}_{1-1-1}||-3^{1}_{-1-11}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(z + \frac{1}{4},-x,y + \frac{1}{4},+1,-v,w,-u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & 1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{4} \\ -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & \frac{1}{4}\end{array}\right]$$
66 $\left\{3^{2}_{1-1-1}||-3^{1}_{-1-11}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(z + \frac{1}{4},\frac{1}{2} - x,y + \frac{3}{4},+1,-v,w,-u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & 1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{3}{4}\end{array}\right]$$
67 $\left\{3^{1}_{-11-1}||-3^{2}_{111}|\frac{1}{2} 0 \frac{1}{2}\right\}$ $(\frac{1}{2} - y,-z,\frac{1}{2} - x,+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0 \\ -1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
68 $\left\{-4^{3}_{100}||-4^{3}_{010}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(z,\frac{1}{4} - y,\frac{1}{4} - x,-1,-u,-w,v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 0 & -1 & 0 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
69 $\left\{3^{1}_{111}||3^{2}_{1-1-1}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(\frac{1}{4} - y,z + \frac{1}{2},\frac{3}{4} - x,+1,w,u,v)$ $$\begin{bmatrix}0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
70 $\left\{-4^{1}_{100}||4^{1}_{010}|\frac{3}{4} \frac{1}{4} \frac{1}{2}\right\}$ $(z + \frac{3}{4},y + \frac{1}{4},\frac{1}{2} - x,-1,-u,w,-v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{3}{4} \\ 0 & 1 & 0 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
71 $\left\{3^{2}_{1-1-1}||-3^{1}_{-1-11}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(z + \frac{3}{4},\frac{1}{2} - x,y + \frac{1}{4},+1,-v,w,-u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & 1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{4}\end{array}\right]$$
72 $\left\{3^{1}_{-11-1}||-3^{2}_{111}|0 0 0\right\}$ $(-y,-z,-x,+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ -1 & 0 & 0 & 0\end{array}\right]$$
73 $\left\{3^{1}_{-1-11}||3^{2}_{-11-1}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(\frac{3}{4} - y,\frac{3}{4} - z,x,+1,-w,u,-v)$ $$\begin{bmatrix}0 & 0 & -1 \\ 1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{3}{4} \\ 1 & 0 & 0 & 0\end{array}\right]$$
74 $\left\{3^{1}_{-1-11}||3^{2}_{-11-1}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(\frac{1}{4} - y,\frac{3}{4} - z,x + \frac{1}{2},+1,-w,u,-v)$ $$\begin{bmatrix}0 & 0 & -1 \\ 1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{3}{4} \\ 1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
75 $\left\{-4^{3}_{010}||4^{1}_{100}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(x + \frac{3}{4},-z,y + \frac{3}{4},-1,w,-v,-u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & 0 \\ 0 & 1 & 0 & \frac{3}{4}\end{array}\right]$$
76 $\left\{2_{001}||m_{001}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(x + \frac{1}{4},y + \frac{3}{4},\frac{1}{2} - z,+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{4} \\ 0 & 1 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
77 $\left\{m_{101}||m_{011}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(x + \frac{1}{2},\frac{1}{4} - z,\frac{3}{4} - y,-1,-w,v,-u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & 1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{3}{4}\end{array}\right]$$
78 $\left\{3^{1}_{-1-11}||3^{2}_{-11-1}|\frac{3}{4} \frac{1}{4} \frac{1}{2}\right\}$ $(\frac{3}{4} - y,\frac{1}{4} - z,x + \frac{1}{2},+1,-w,u,-v)$ $$\begin{bmatrix}0 & 0 & -1 \\ 1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
79 $\left\{3^{1}_{-11-1}||-3^{2}_{111}|0 \frac{1}{2} \frac{1}{2}\right\}$ $(-y,\frac{1}{2} - z,\frac{1}{2} - x,+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
80 $\left\{-4^{3}_{010}||4^{1}_{100}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(x + \frac{1}{4},\frac{1}{2} - z,y + \frac{3}{4},-1,w,-v,-u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{3}{4}\end{array}\right]$$
81 $\left\{3^{1}_{-11-1}||-3^{2}_{111}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - y,\frac{1}{2} - z,-x,+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{1}{2} \\ -1 & 0 & 0 & 0\end{array}\right]$$
82 $\left\{2_{001}||m_{001}|\frac{3}{4} \frac{1}{4} \frac{1}{2}\right\}$ $(x + \frac{3}{4},y + \frac{1}{4},\frac{1}{2} - z,+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{3}{4} \\ 0 & 1 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
83 $\left\{m_{101}||m_{011}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(x,\frac{3}{4} - z,\frac{3}{4} - y,-1,-w,v,-u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & 1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 0 & -1 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{3}{4}\end{array}\right]$$
84 $\left\{3^{1}_{-1-11}||3^{2}_{-11-1}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(\frac{1}{4} - y,\frac{1}{4} - z,x,+1,-w,u,-v)$ $$\begin{bmatrix}0 & 0 & -1 \\ 1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{4} \\ 1 & 0 & 0 & 0\end{array}\right]$$
85 $\left\{-4^{1}_{001}||4^{1}_{001}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(-y,x + \frac{1}{4},z + \frac{1}{4},-1,v,-u,-w)$ $$\begin{bmatrix}0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ 1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{1}{4}\end{array}\right]$$
86 $\left\{-4^{1}_{010}||4^{3}_{100}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(x + \frac{1}{4},z + \frac{3}{4},\frac{1}{2} - y,-1,-w,-v,u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & -1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{1}{2}\end{array}\right]$$
87 $\left\{m_{1-10}||m_{110}|\frac{3}{4} \frac{1}{4} \frac{1}{2}\right\}$ $(\frac{3}{4} - y,\frac{1}{4} - x,z + \frac{1}{2},-1,v,u,w)$ $$\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
88 $\left\{m_{1-10}||m_{110}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(\frac{3}{4} - y,\frac{3}{4} - x,z,-1,v,u,w)$ $$\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & 0\end{array}\right]$$
89 $\left\{m_{101}||m_{011}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(x,\frac{1}{4} - z,\frac{1}{4} - y,-1,-w,v,-u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & 1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{1}{4}\end{array}\right]$$
90 $\left\{2_{100}||m_{010}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(x + \frac{1}{4},\frac{1}{2} - y,z + \frac{3}{4},+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{3}{4}\end{array}\right]$$
91 $\left\{-4^{1}_{001}||4^{1}_{001}|\frac{1}{2} \frac{3}{4} \frac{1}{4}\right\}$ $(\frac{1}{2} - y,x + \frac{3}{4},z + \frac{1}{4},-1,v,-u,-w)$ $$\begin{bmatrix}0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{1}{4}\end{array}\right]$$
92 $\left\{-4^{1}_{001}||4^{1}_{001}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(-y,x + \frac{3}{4},z + \frac{3}{4},-1,v,-u,-w)$ $$\begin{bmatrix}0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ 1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{3}{4}\end{array}\right]$$
93 $\left\{-4^{1}_{001}||4^{1}_{001}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(\frac{1}{2} - y,x + \frac{1}{4},z + \frac{3}{4},-1,v,-u,-w)$ $$\begin{bmatrix}0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{3}{4}\end{array}\right]$$
94 $\left\{-4^{1}_{010}||4^{3}_{100}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(x + \frac{3}{4},z + \frac{3}{4},-y,-1,-w,-v,u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & -1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{3}{4} \\ 0 & -1 & 0 & 0\end{array}\right]$$
95 $\left\{2_{100}||m_{010}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(x + \frac{3}{4},\frac{1}{2} - y,z + \frac{1}{4},+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{4}\end{array}\right]$$
96 $\left\{3^{1}_{1-1-1}||-3^{2}_{-1-11}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(\frac{1}{2} - y,z + \frac{1}{4},x + \frac{3}{4},+1,-w,-u,v)$ $$\begin{bmatrix}0 & 0 & -1 \\ -1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
97 $\left\{-4^{1}_{010}||4^{3}_{100}|\frac{3}{4} \frac{1}{4} \frac{1}{2}\right\}$ $(x + \frac{3}{4},z + \frac{1}{4},\frac{1}{2} - y,-1,-w,-v,u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & -1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{1}{2}\end{array}\right]$$
98 $\left\{-4^{1}_{010}||4^{3}_{100}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(x + \frac{1}{4},z + \frac{1}{4},-y,-1,-w,-v,u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & -1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{1}{4} \\ 0 & -1 & 0 & 0\end{array}\right]$$
99 $\left\{m_{01-1}||2_{101}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(z + \frac{3}{4},\frac{1}{2} - y,x + \frac{1}{4},-1,u,w,v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
100 $\left\{-4^{3}_{010}||-4^{1}_{100}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(\frac{1}{4} - x,z + \frac{1}{2},\frac{3}{4} - y,-1,w,-v,-u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{3}{4}\end{array}\right]$$
101 $\left\{-4^{3}_{010}||-4^{1}_{100}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(\frac{3}{4} - x,z,\frac{3}{4} - y,-1,w,-v,-u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & 0 \\ 0 & -1 & 0 & \frac{3}{4}\end{array}\right]$$
102 $\left\{-4^{1}_{100}||-4^{1}_{010}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(\frac{1}{4} - z,\frac{1}{4} - y,x,-1,-u,w,-v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{1}{4} \\ 1 & 0 & 0 & 0\end{array}\right]$$
103 $\left\{3^{1}_{1-1-1}||-3^{2}_{-1-11}|\frac{1}{2} \frac{3}{4} \frac{1}{4}\right\}$ $(\frac{1}{2} - y,z + \frac{3}{4},x + \frac{1}{4},+1,-w,-u,v)$ $$\begin{bmatrix}0 & 0 & -1 \\ -1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{3}{4} \\ 1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
104 $\left\{m_{01-1}||2_{101}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(z + \frac{3}{4},-y,x + \frac{3}{4},-1,u,w,v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{3}{4} \\ 0 & -1 & 0 & 0 \\ 1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
105 $\left\{m_{011}||2_{-101}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - z,\frac{1}{2} - y,-x,-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & 0\end{array}\right]$$
106 $\left\{m_{1-10}||2_{110}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(y + \frac{1}{4},x + \frac{3}{4},\frac{1}{2} - z,-1,v,u,w)$ $$\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
107 $\left\{-4^{1}_{100}||-4^{1}_{010}|\frac{3}{4} \frac{1}{4} \frac{1}{2}\right\}$ $(\frac{3}{4} - z,\frac{1}{4} - y,x + \frac{1}{2},-1,-u,w,-v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
108 $\left\{m_{110}||m_{1-10}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(y + \frac{1}{2},x + \frac{1}{2},z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0\end{array}\right]$$
109 $\left\{3^{2}_{-1-11}||-3^{1}_{-11-1}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(-z,x + \frac{3}{4},y + \frac{3}{4},+1,v,-w,-u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & -1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & 0 \\ 1 & 0 & 0 & \frac{3}{4} \\ 0 & 1 & 0 & \frac{3}{4}\end{array}\right]$$
110 $\left\{m_{011}||2_{-101}|\frac{1}{2} 0 \frac{1}{2}\right\}$ $(\frac{1}{2} - z,-y,\frac{1}{2} - x,-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{2} \\ 0 & -1 & 0 & 0 \\ -1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
111 $\left\{m_{011}||2_{-101}|0 \frac{1}{2} \frac{1}{2}\right\}$ $(-z,\frac{1}{2} - y,\frac{1}{2} - x,-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & 0 \\ 0 & -1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
112 $\left\{m_{011}||2_{-101}|0 0 0\right\}$ $(-z,-y,-x,-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & 0 \\ 0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0\end{array}\right]$$
113 $\left\{m_{110}||m_{1-10}|0 0 0\right\}$ $(y,x,z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
114 $\left\{m_{1-10}||2_{110}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(y + \frac{1}{4},x + \frac{1}{4},-z,-1,v,u,w)$ $$\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & 0\end{array}\right]$$
115 $\left\{m_{101}||2_{011}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(\frac{1}{2} - x,z + \frac{1}{4},y + \frac{3}{4},-1,-w,v,-u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & 1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{4} \\ 0 & 1 & 0 & \frac{3}{4}\end{array}\right]$$
116 $\left\{2_{100}||2_{010}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(\frac{1}{4} - x,y,\frac{1}{4} - z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{4} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{4}\end{array}\right]$$
117 $\left\{-4^{1}_{001}||-4^{1}_{001}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(y,\frac{3}{4} - x,\frac{3}{4} - z,-1,v,-u,-w)$ $$\begin{bmatrix}0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ -1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{3}{4}\end{array}\right]$$
118 $\left\{-4^{1}_{001}||-4^{1}_{001}|\frac{1}{2} \frac{3}{4} \frac{1}{4}\right\}$ $(y + \frac{1}{2},\frac{3}{4} - x,\frac{1}{4} - z,-1,v,-u,-w)$ $$\begin{bmatrix}0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{1}{4}\end{array}\right]$$
119 $\left\{-4^{1}_{001}||-4^{1}_{001}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(y,\frac{1}{4} - x,\frac{1}{4} - z,-1,v,-u,-w)$ $$\begin{bmatrix}0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ -1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{4}\end{array}\right]$$
120 $\left\{-4^{1}_{010}||-4^{3}_{100}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(\frac{3}{4} - x,\frac{3}{4} - z,y,-1,-w,-v,u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & -1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{3}{4} \\ 0 & 1 & 0 & 0\end{array}\right]$$
121 $\left\{2_{100}||2_{010}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(\frac{3}{4} - x,y,\frac{3}{4} - z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{4} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{3}{4}\end{array}\right]$$
122 $\left\{-4^{1}_{001}||-4^{1}_{001}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(y + \frac{1}{2},\frac{1}{4} - x,\frac{3}{4} - z,-1,v,-u,-w)$ $$\begin{bmatrix}0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{3}{4}\end{array}\right]$$
123 $\left\{-4^{1}_{010}||-4^{3}_{100}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(\frac{1}{4} - x,\frac{3}{4} - z,y + \frac{1}{2},-1,-w,-v,u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & -1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{3}{4} \\ 0 & 1 & 0 & \frac{1}{2}\end{array}\right]$$
124 $\left\{-4^{1}_{010}||-4^{3}_{100}|\frac{3}{4} \frac{1}{4} \frac{1}{2}\right\}$ $(\frac{3}{4} - x,\frac{1}{4} - z,y + \frac{1}{2},-1,-w,-v,u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & -1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{1}{4} \\ 0 & 1 & 0 & \frac{1}{2}\end{array}\right]$$
125 $\left\{3^{1}_{1-1-1}||3^{2}_{-1-11}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(y,\frac{1}{4} - z,\frac{1}{4} - x,+1,-w,-u,v)$ $$\begin{bmatrix}0 & 0 & -1 \\ -1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
126 $\left\{-4^{1}_{010}||-4^{3}_{100}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(\frac{1}{4} - x,\frac{1}{4} - z,y,-1,-w,-v,u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & -1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{4} \\ 0 & 1 & 0 & 0\end{array}\right]$$
127 $\left\{m_{01-1}||m_{101}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(\frac{3}{4} - z,y,\frac{3}{4} - x,-1,u,w,v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{3}{4} \\ 0 & 1 & 0 & 0 \\ -1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
128 $\left\{-4^{3}_{010}||4^{1}_{100}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(x + \frac{1}{4},-z,y + \frac{1}{4},-1,w,-v,-u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & 0 \\ 0 & 1 & 0 & \frac{1}{4}\end{array}\right]$$
129 $\left\{-4^{3}_{010}||4^{1}_{100}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(x + \frac{3}{4},\frac{1}{2} - z,y + \frac{1}{4},-1,w,-v,-u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{4}\end{array}\right]$$
130 $\left\{3^{1}_{1-1-1}||3^{2}_{-1-11}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(y,\frac{3}{4} - z,\frac{3}{4} - x,+1,-w,-u,v)$ $$\begin{bmatrix}0 & 0 & -1 \\ -1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
131 $\left\{m_{01-1}||m_{101}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(\frac{3}{4} - z,y + \frac{1}{2},\frac{1}{4} - x,-1,u,w,v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{3}{4} \\ 0 & 1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
132 $\left\{-4^{1}_{100}||4^{1}_{010}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(z + \frac{1}{4},y + \frac{3}{4},\frac{1}{2} - x,-1,-u,w,-v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{4} \\ 0 & 1 & 0 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
133 $\left\{m_{011}||m_{-101}|\frac{1}{2} 0 \frac{1}{2}\right\}$ $(z + \frac{1}{2},y,x + \frac{1}{2},-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{2} \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
134 $\left\{m_{011}||m_{-101}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(z + \frac{1}{2},y + \frac{1}{2},x,-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & 0\end{array}\right]$$
135 $\left\{m_{110}||2_{1-10}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - y,\frac{1}{2} - x,-z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0\end{array}\right]$$
136 $\left\{3^{2}_{-1-11}||3^{1}_{-11-1}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(z,\frac{1}{4} - x,\frac{1}{4} - y,+1,v,-w,-u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & -1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ -1 & 0 & 0 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{1}{4}\end{array}\right]$$
137 $\left\{m_{011}||m_{-101}|0 0 0\right\}$ $(z,y,x,-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$
138 $\left\{-4^{1}_{100}||4^{1}_{010}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(z + \frac{3}{4},y + \frac{3}{4},-x,-1,-u,w,-v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{3}{4} \\ 0 & 1 & 0 & \frac{3}{4} \\ -1 & 0 & 0 & 0\end{array}\right]$$
139 $\left\{m_{110}||2_{1-10}|0 0 0\right\}$ $(-y,-x,-z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
140 $\left\{m_{011}||m_{-101}|0 \frac{1}{2} \frac{1}{2}\right\}$ $(z,y + \frac{1}{2},x + \frac{1}{2},-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 0 & 1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{1}{2}\end{array}\right]$$
141 $\left\{-4^{3}_{100}||-4^{3}_{010}|\frac{1}{2} \frac{3}{4} \frac{1}{4}\right\}$ $(z + \frac{1}{2},\frac{3}{4} - y,\frac{1}{4} - x,-1,-u,-w,v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
142 $\left\{3^{1}_{111}||3^{2}_{1-1-1}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(\frac{3}{4} - y,z,\frac{3}{4} - x,+1,w,u,v)$ $$\begin{bmatrix}0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & 0 \\ -1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
143 $\left\{3^{2}_{-1-11}||3^{1}_{-11-1}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(z,\frac{3}{4} - x,\frac{3}{4} - y,+1,v,-w,-u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & -1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ -1 & 0 & 0 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{3}{4}\end{array}\right]$$
144 $\left\{-4^{3}_{001}||4^{3}_{001}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(y + \frac{3}{4},\frac{1}{2} - x,z + \frac{1}{4},-1,-v,u,-w)$ $$\begin{bmatrix}0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{4}\end{array}\right]$$
145 $\left\{-4^{3}_{001}||4^{3}_{001}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(y + \frac{3}{4},-x,z + \frac{3}{4},-1,-v,u,-w)$ $$\begin{bmatrix}0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{3}{4} \\ -1 & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{3}{4}\end{array}\right]$$
146 $\left\{-4^{3}_{100}||4^{3}_{010}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(-z,y + \frac{1}{4},x + \frac{1}{4},-1,-u,-w,v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & 0 \\ 0 & 1 & 0 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
147 $\left\{3^{1}_{111}||-3^{2}_{1-1-1}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(y + \frac{3}{4},-z,x + \frac{3}{4},+1,w,u,v)$ $$\begin{bmatrix}0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & 0 \\ 1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
148 $\left\{-4^{3}_{100}||4^{3}_{010}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(\frac{1}{2} - z,y + \frac{1}{4},x + \frac{3}{4},-1,-u,-w,v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
149 $\left\{3^{1}_{111}||-3^{2}_{1-1-1}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(y + \frac{1}{4},-z,x + \frac{1}{4},+1,w,u,v)$ $$\begin{bmatrix}0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & 0 \\ 1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
150 $\left\{3^{2}_{-1-11}||-3^{1}_{-11-1}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(-z,x + \frac{1}{4},y + \frac{1}{4},+1,v,-w,-u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & -1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & 0 \\ 1 & 0 & 0 & \frac{1}{4} \\ 0 & 1 & 0 & \frac{1}{4}\end{array}\right]$$
151 $\left\{-4^{3}_{001}||-4^{3}_{001}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(\frac{1}{4} - y,x + \frac{1}{2},\frac{3}{4} - z,-1,-v,u,-w)$ $$\begin{bmatrix}0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{3}{4}\end{array}\right]$$
152 $\left\{-4^{3}_{001}||-4^{3}_{001}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(\frac{1}{4} - y,x,\frac{1}{4} - z,-1,-v,u,-w)$ $$\begin{bmatrix}0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{4} \\ 1 & 0 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{4}\end{array}\right]$$
153 $\left\{-4^{3}_{100}||-4^{3}_{010}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(z,\frac{3}{4} - y,\frac{3}{4} - x,-1,-u,-w,v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 0 & -1 & 0 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
154 $\left\{3^{1}_{111}||3^{2}_{1-1-1}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(\frac{1}{4} - y,z,\frac{1}{4} - x,+1,w,u,v)$ $$\begin{bmatrix}0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & 0 \\ -1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
155 $\left\{3^{1}_{1-1-1}||3^{2}_{-1-11}|\frac{1}{2} \frac{1}{4} \frac{3}{4}\right\}$ $(y + \frac{1}{2},\frac{1}{4} - z,\frac{3}{4} - x,+1,-w,-u,v)$ $$\begin{bmatrix}0 & 0 & -1 \\ -1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
156 $\left\{m_{01-1}||m_{101}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(\frac{1}{4} - z,y,\frac{1}{4} - x,-1,u,w,v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{4} \\ 0 & 1 & 0 & 0 \\ -1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
157 $\left\{m_{101}||m_{011}|\frac{1}{2} \frac{3}{4} \frac{1}{4}\right\}$ $(x + \frac{1}{2},\frac{3}{4} - z,\frac{1}{4} - y,-1,-w,v,-u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & 1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{1}{4}\end{array}\right]$$
158 $\left\{2_{100}||m_{010}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(x + \frac{3}{4},-y,z + \frac{3}{4},+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{3}{4} \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 1 & \frac{3}{4}\end{array}\right]$$
159 $\left\{2_{100}||m_{010}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(x + \frac{1}{4},-y,z + \frac{1}{4},+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{4} \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{4}\end{array}\right]$$
160 $\left\{3^{1}_{1-1-1}||-3^{2}_{-1-11}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(-y,z + \frac{3}{4},x + \frac{3}{4},+1,-w,-u,v)$ $$\begin{bmatrix}0 & 0 & -1 \\ -1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ 0 & 0 & 1 & \frac{3}{4} \\ 1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
161 $\left\{m_{01-1}||2_{101}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(z + \frac{1}{4},-y,x + \frac{1}{4},-1,u,w,v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{4} \\ 0 & -1 & 0 & 0 \\ 1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
162 $\left\{3^{1}_{1-1-1}||-3^{2}_{-1-11}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(-y,z + \frac{1}{4},x + \frac{1}{4},+1,-w,-u,v)$ $$\begin{bmatrix}0 & 0 & -1 \\ -1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
163 $\left\{m_{01-1}||2_{101}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(z + \frac{1}{4},\frac{1}{2} - y,x + \frac{3}{4},-1,u,w,v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
164 $\left\{m_{101}||2_{011}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(-x,z + \frac{3}{4},y + \frac{3}{4},-1,-w,v,-u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & 1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{3}{4} \\ 0 & 1 & 0 & \frac{3}{4}\end{array}\right]$$
165 $\left\{2_{100}||2_{010}|\frac{3}{4} \frac{1}{2} \frac{1}{4}\right\}$ $(\frac{3}{4} - x,y + \frac{1}{2},\frac{1}{4} - z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{4} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{1}{4}\end{array}\right]$$
166 $\left\{2_{100}||2_{010}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(\frac{1}{4} - x,y + \frac{1}{2},\frac{3}{4} - z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{4} \\ 0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{3}{4}\end{array}\right]$$
167 $\left\{3^{1}_{1-1-1}||3^{2}_{-1-11}|\frac{1}{2} \frac{3}{4} \frac{1}{4}\right\}$ $(y + \frac{1}{2},\frac{3}{4} - z,\frac{1}{4} - x,+1,-w,-u,v)$ $$\begin{bmatrix}0 & 0 & -1 \\ -1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
168 $\left\{m_{01-1}||m_{101}|\frac{1}{4} \frac{1}{2} \frac{3}{4}\right\}$ $(\frac{1}{4} - z,y + \frac{1}{2},\frac{3}{4} - x,-1,u,w,v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{4} \\ 0 & 1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
169 $\left\{2_{001}||2_{001}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(\frac{3}{4} - x,\frac{3}{4} - y,z,+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & 0\end{array}\right]$$
170 $\left\{2_{001}||2_{001}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(\frac{1}{4} - x,\frac{1}{4} - y,z,+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & 0\end{array}\right]$$
171 $\left\{2_{001}||m_{001}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(x + \frac{3}{4},y + \frac{3}{4},-z,+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{3}{4} \\ 0 & 1 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & 0\end{array}\right]$$
172 $\left\{2_{001}||m_{001}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(x + \frac{1}{4},y + \frac{1}{4},-z,+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{4} \\ 0 & 1 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & 0\end{array}\right]$$
173 $\left\{m_{110}||m_{1-10}|0 \frac{1}{2} \frac{1}{2}\right\}$ $(y,x + \frac{1}{2},z + \frac{1}{2},-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
174 $\left\{m_{110}||m_{1-10}|\frac{1}{2} 0 \frac{1}{2}\right\}$ $(y + \frac{1}{2},x,z + \frac{1}{2},-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & \frac{1}{2} \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{2}\end{array}\right]$$
175 $\left\{m_{110}||2_{1-10}|0 \frac{1}{2} \frac{1}{2}\right\}$ $(-y,\frac{1}{2} - x,\frac{1}{2} - z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ -1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
176 $\left\{m_{110}||2_{1-10}|\frac{1}{2} 0 \frac{1}{2}\right\}$ $(\frac{1}{2} - y,-x,\frac{1}{2} - z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{2} \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{2}\end{array}\right]$$
177 $\left\{3^{2}_{111}||-3^{1}_{1-1-1}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(z + \frac{1}{4},x + \frac{3}{4},\frac{1}{2} - y,+1,v,w,u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{1}{2}\end{array}\right]$$
178 $\left\{3^{2}_{111}||-3^{1}_{1-1-1}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(z + \frac{1}{4},x + \frac{1}{4},-y,+1,v,w,u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{1}{4} \\ 1 & 0 & 0 & \frac{1}{4} \\ 0 & -1 & 0 & 0\end{array}\right]$$
179 $\left\{3^{2}_{111}||-3^{1}_{1-1-1}|\frac{3}{4} \frac{1}{4} \frac{1}{2}\right\}$ $(z + \frac{3}{4},x + \frac{1}{4},\frac{1}{2} - y,+1,v,w,u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{3}{4} \\ 1 & 0 & 0 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{1}{2}\end{array}\right]$$
180 $\left\{3^{2}_{111}||-3^{1}_{1-1-1}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(z + \frac{3}{4},x + \frac{3}{4},-y,+1,v,w,u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & \frac{3}{4} \\ 1 & 0 & 0 & \frac{3}{4} \\ 0 & -1 & 0 & 0\end{array}\right]$$
181 $\left\{m_{-101}||m_{01-1}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(x + \frac{1}{2},z + \frac{1}{2},y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & \frac{1}{2} \\ 0 & 1 & 0 & 0\end{array}\right]$$
182 $\left\{m_{-101}||m_{01-1}|0 0 0\right\}$ $(x,z,y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0\end{array}\right]$$
183 $\left\{3^{2}_{111}||3^{1}_{1-1-1}|\frac{3}{4} \frac{1}{4} \frac{1}{2}\right\}$ $(\frac{3}{4} - z,\frac{1}{4} - x,y + \frac{1}{2},+1,v,w,u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{1}{4} \\ 0 & 1 & 0 & \frac{1}{2}\end{array}\right]$$
184 $\left\{3^{2}_{111}||3^{1}_{1-1-1}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(\frac{1}{4} - z,\frac{1}{4} - x,y,+1,v,w,u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{1}{4} \\ 0 & 1 & 0 & 0\end{array}\right]$$
185 $\left\{3^{2}_{111}||3^{1}_{1-1-1}|\frac{1}{4} \frac{3}{4} \frac{1}{2}\right\}$ $(\frac{1}{4} - z,\frac{3}{4} - x,y + \frac{1}{2},+1,v,w,u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{3}{4} \\ 0 & 1 & 0 & \frac{1}{2}\end{array}\right]$$
186 $\left\{3^{2}_{111}||3^{1}_{1-1-1}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(\frac{3}{4} - z,\frac{3}{4} - x,y,+1,v,w,u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{3}{4} \\ 0 & 1 & 0 & 0\end{array}\right]$$
187 $\left\{m_{-101}||2_{01-1}|0 \frac{1}{2} \frac{1}{2}\right\}$ $(-x,\frac{1}{2} - z,\frac{1}{2} - y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{2} \\ 0 & -1 & 0 & \frac{1}{2}\end{array}\right]$$
188 $\left\{m_{-101}||2_{01-1}|\frac{1}{2} 0 \frac{1}{2}\right\}$ $(\frac{1}{2} - x,-z,\frac{1}{2} - y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & 0 \\ 0 & -1 & 0 & \frac{1}{2}\end{array}\right]$$
189 $\left\{m_{-101}||2_{01-1}|\frac{1}{2} \frac{1}{2} 0\right\}$ $(\frac{1}{2} - x,\frac{1}{2} - z,-y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & -1 & \frac{1}{2} \\ 0 & -1 & 0 & 0\end{array}\right]$$
190 $\left\{m_{-101}||m_{01-1}|0 \frac{1}{2} \frac{1}{2}\right\}$ $(x,z + \frac{1}{2},y + \frac{1}{2},-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{1}{2} \\ 0 & 1 & 0 & \frac{1}{2}\end{array}\right]$$
191 $\left\{m_{-101}||2_{01-1}|0 0 0\right\}$ $(-x,-z,-y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & -1 & 0 & 0\end{array}\right]$$
192 $\left\{m_{-101}||m_{01-1}|\frac{1}{2} 0 \frac{1}{2}\right\}$ $(x + \frac{1}{2},z,y + \frac{1}{2},-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1}{2} \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & \frac{1}{2}\end{array}\right]$$
wyckoff position site symmetry Coordinates
$(0,0,0\mid mx,my,mz)+(\frac{1}{2},\frac{1}{2},0\mid mx,my,mz)+(\frac{1}{2},0,\frac{1}{2}\mid mx,my,mz)+(0,\frac{1}{2},\frac{1}{2}\mid mx,my,mz)$
192i $(x,y,z\mid mx,my,mz),(\frac{3}{4} - x,\frac{1}{4} - y,z + \frac{1}{2}\mid -mx,-my,mz),(\frac{1}{4} - x,y + \frac{1}{2},\frac{3}{4} - z\mid mx,-my,-mz),(x + \frac{1}{2},\frac{3}{4} - y,\frac{1}{4} - z\mid -mx,my,-mz),(z,x,y\mid -my,-mz,mx),(z + \frac{1}{2},\frac{3}{4} - x,\frac{1}{4} - y\mid my,-mz,-mx),(\frac{3}{4} - z,\frac{1}{4} - x,y + \frac{1}{2}\mid my,mz,mx),(\frac{1}{4} - z,x + \frac{1}{2},\frac{3}{4} - y\mid -my,mz,-mx),(y,z,x\mid mz,-mx,-my),(\frac{1}{4} - y,z + \frac{1}{2},\frac{3}{4} - x\mid mz,mx,my),(y + \frac{1}{2},\frac{3}{4} - z,\frac{1}{4} - x\mid -mz,-mx,my),(\frac{3}{4} - y,\frac{1}{4} - z,x + \frac{1}{2}\mid -mz,mx,-my),(y + \frac{3}{4},x + \frac{1}{4},\frac{1}{2} - z\mid my,mx,mz),(-y,-x,-z\mid -my,-mx,mz),(y + \frac{1}{4},\frac{1}{2} - x,z + \frac{3}{4}\mid -my,mx,-mz),(\frac{1}{2} - y,x + \frac{3}{4},z + \frac{1}{4}\mid my,-mx,-mz),(x + \frac{3}{4},z + \frac{1}{4},\frac{1}{2} - y\mid -mz,-my,mx),(\frac{1}{2} - x,z + \frac{3}{4},y + \frac{1}{4}\mid -mz,my,-mx),(-x,-z,-y\mid mz,my,mx),(x + \frac{1}{4},\frac{1}{2} - z,y + \frac{3}{4}\mid mz,-my,-mx),(z + \frac{3}{4},y + \frac{1}{4},\frac{1}{2} - x\mid -mx,mz,-my),(z + \frac{1}{4},\frac{1}{2} - y,x + \frac{3}{4}\mid mx,mz,my),(\frac{1}{2} - z,y + \frac{3}{4},x + \frac{1}{4}\mid -mx,-mz,my),(-z,-y,-x\mid mx,-mz,-my),(-x,-y,-z\mid mx,my,mz),(x + \frac{1}{4},y + \frac{3}{4},\frac{1}{2} - z\mid -mx,-my,mz),(x + \frac{3}{4},\frac{1}{2} - y,z + \frac{1}{4}\mid mx,-my,-mz),(\frac{1}{2} - x,y + \frac{1}{4},z + \frac{3}{4}\mid -mx,my,-mz),(-z,-x,-y\mid -my,-mz,mx),(\frac{1}{2} - z,x + \frac{1}{4},y + \frac{3}{4}\mid my,-mz,-mx),(z + \frac{1}{4},x + \frac{3}{4},\frac{1}{2} - y\mid my,mz,mx),(z + \frac{3}{4},\frac{1}{2} - x,y + \frac{1}{4}\mid -my,mz,-mx),(-y,-z,-x\mid mz,-mx,-my),(y + \frac{3}{4},\frac{1}{2} - z,x + \frac{1}{4}\mid mz,mx,my),(\frac{1}{2} - y,z + \frac{1}{4},x + \frac{3}{4}\mid -mz,-mx,my),(y + \frac{1}{4},z + \frac{3}{4},\frac{1}{2} - x\mid -mz,mx,-my),(\frac{1}{4} - y,\frac{3}{4} - x,z + \frac{1}{2}\mid my,mx,mz),(y,x,z\mid -my,-mx,mz),(\frac{3}{4} - y,x + \frac{1}{2},\frac{1}{4} - z\mid -my,mx,-mz),(y + \frac{1}{2},\frac{1}{4} - x,\frac{3}{4} - z\mid my,-mx,-mz),(\frac{1}{4} - x,\frac{3}{4} - z,y + \frac{1}{2}\mid -mz,-my,mx),(x + \frac{1}{2},\frac{1}{4} - z,\frac{3}{4} - y\mid -mz,my,-mx),(x,z,y\mid mz,my,mx),(\frac{3}{4} - x,z + \frac{1}{2},\frac{1}{4} - y\mid mz,-my,-mx),(\frac{1}{4} - z,\frac{3}{4} - y,x + \frac{1}{2}\mid -mx,mz,-my),(\frac{3}{4} - z,y + \frac{1}{2},\frac{1}{4} - x\mid mx,mz,my),(z + \frac{1}{2},\frac{1}{4} - y,\frac{3}{4} - x\mid -mx,-mz,my),(z,y,x\mid mx,-mz,-my)$
96h $(0,y,-y\mid \sqrt{2} my/2,mx,\sqrt{2} my/2),(\frac{3}{4},\frac{1}{4} - y,\frac{1}{2} - y\mid -\sqrt{2} my/2,-mx,\sqrt{2} my/2),(\frac{1}{4},y + \frac{1}{2},y + \frac{3}{4}\mid \sqrt{2} my/2,-mx,-\sqrt{2} my/2),(\frac{1}{2},\frac{3}{4} - y,y + \frac{1}{4}\mid -\sqrt{2} my/2,mx,-\sqrt{2} my/2),(-y,0,y\mid -mx,-\sqrt{2} my/2,\sqrt{2} my/2),(\frac{1}{2} - y,\frac{3}{4},\frac{1}{4} - y\mid mx,-\sqrt{2} my/2,-\sqrt{2} my/2),(y + \frac{3}{4},\frac{1}{4},y + \frac{1}{2}\mid mx,\sqrt{2} my/2,\sqrt{2} my/2),(y + \frac{1}{4},\frac{1}{2},\frac{3}{4} - y\mid -mx,\sqrt{2} my/2,-\sqrt{2} my/2),(y,-y,0\mid \sqrt{2} my/2,-\sqrt{2} my/2,-mx),(\frac{1}{4} - y,\frac{1}{2} - y,\frac{3}{4}\mid \sqrt{2} my/2,\sqrt{2} my/2,mx),(y + \frac{1}{2},y + \frac{3}{4},\frac{1}{4}\mid -\sqrt{2} my/2,-\sqrt{2} my/2,mx),(\frac{3}{4} - y,y + \frac{1}{4},\frac{1}{2}\mid -\sqrt{2} my/2,\sqrt{2} my/2,-mx),(0,-y,y\mid \sqrt{2} my/2,mx,\sqrt{2} my/2),(\frac{1}{4},y + \frac{3}{4},y + \frac{1}{2}\mid -\sqrt{2} my/2,-mx,\sqrt{2} my/2),(\frac{3}{4},\frac{1}{2} - y,\frac{1}{4} - y\mid \sqrt{2} my/2,-mx,-\sqrt{2} my/2),(\frac{1}{2},y + \frac{1}{4},\frac{3}{4} - y\mid -\sqrt{2} my/2,mx,-\sqrt{2} my/2),(y,0,-y\mid -mx,-\sqrt{2} my/2,\sqrt{2} my/2),(y + \frac{1}{2},\frac{1}{4},y + \frac{3}{4}\mid mx,-\sqrt{2} my/2,-\sqrt{2} my/2),(\frac{1}{4} - y,\frac{3}{4},\frac{1}{2} - y\mid mx,\sqrt{2} my/2,\sqrt{2} my/2),(\frac{3}{4} - y,\frac{1}{2},y + \frac{1}{4}\mid -mx,\sqrt{2} my/2,-\sqrt{2} my/2),(-y,y,0\mid \sqrt{2} my/2,-\sqrt{2} my/2,-mx),(y + \frac{3}{4},y + \frac{1}{2},\frac{1}{4}\mid \sqrt{2} my/2,\sqrt{2} my/2,mx),(\frac{1}{2} - y,\frac{1}{4} - y,\frac{3}{4}\mid -\sqrt{2} my/2,-\sqrt{2} my/2,mx),(y + \frac{1}{4},\frac{3}{4} - y,\frac{1}{2}\mid -\sqrt{2} my/2,\sqrt{2} my/2,-mx)$
96g $(x,x,z\mid -\sqrt{2} mx/2,\sqrt{2} mx/2,my),(\frac{3}{4} - x,\frac{1}{4} - x,z + \frac{1}{2}\mid \sqrt{2} mx/2,-\sqrt{2} mx/2,my),(\frac{1}{4} - x,x + \frac{1}{2},\frac{3}{4} - z\mid -\sqrt{2} mx/2,-\sqrt{2} mx/2,-my),(x + \frac{1}{2},\frac{3}{4} - x,\frac{1}{4} - z\mid \sqrt{2} mx/2,\sqrt{2} mx/2,-my),(z,x,x\mid -\sqrt{2} mx/2,-my,-\sqrt{2} mx/2),(z + \frac{1}{2},\frac{3}{4} - x,\frac{1}{4} - x\mid \sqrt{2} mx/2,-my,\sqrt{2} mx/2),(\frac{3}{4} - z,\frac{1}{4} - x,x + \frac{1}{2}\mid \sqrt{2} mx/2,my,-\sqrt{2} mx/2),(\frac{1}{4} - z,x + \frac{1}{2},\frac{3}{4} - x\mid -\sqrt{2} mx/2,my,\sqrt{2} mx/2),(x,z,x\mid my,\sqrt{2} mx/2,-\sqrt{2} mx/2),(\frac{1}{4} - x,z + \frac{1}{2},\frac{3}{4} - x\mid my,-\sqrt{2} mx/2,\sqrt{2} mx/2),(x + \frac{1}{2},\frac{3}{4} - z,\frac{1}{4} - x\mid -my,\sqrt{2} mx/2,\sqrt{2} mx/2),(\frac{3}{4} - x,\frac{1}{4} - z,x + \frac{1}{2}\mid -my,-\sqrt{2} mx/2,-\sqrt{2} mx/2),(x + \frac{3}{4},x + \frac{1}{4},\frac{1}{2} - z\mid \sqrt{2} mx/2,-\sqrt{2} mx/2,my),(-x,-x,-z\mid -\sqrt{2} mx/2,\sqrt{2} mx/2,my),(x + \frac{1}{4},\frac{1}{2} - x,z + \frac{3}{4}\mid -\sqrt{2} mx/2,-\sqrt{2} mx/2,-my),(\frac{1}{2} - x,x + \frac{3}{4},z + \frac{1}{4}\mid \sqrt{2} mx/2,\sqrt{2} mx/2,-my),(x + \frac{3}{4},z + \frac{1}{4},\frac{1}{2} - x\mid -my,-\sqrt{2} mx/2,-\sqrt{2} mx/2),(\frac{1}{2} - x,z + \frac{3}{4},x + \frac{1}{4}\mid -my,\sqrt{2} mx/2,\sqrt{2} mx/2),(-x,-z,-x\mid my,\sqrt{2} mx/2,-\sqrt{2} mx/2),(x + \frac{1}{4},\frac{1}{2} - z,x + \frac{3}{4}\mid my,-\sqrt{2} mx/2,\sqrt{2} mx/2),(z + \frac{3}{4},x + \frac{1}{4},\frac{1}{2} - x\mid \sqrt{2} mx/2,my,-\sqrt{2} mx/2),(z + \frac{1}{4},\frac{1}{2} - x,x + \frac{3}{4}\mid -\sqrt{2} mx/2,my,\sqrt{2} mx/2),(\frac{1}{2} - z,x + \frac{3}{4},x + \frac{1}{4}\mid \sqrt{2} mx/2,-my,\sqrt{2} mx/2),(-z,-x,-x\mid -\sqrt{2} mx/2,-my,-\sqrt{2} mx/2)$
48f $(x,\frac{1}{8},\frac{1}{8}\mid 0,mx,0),(\frac{3}{4} - x,\frac{1}{8},\frac{5}{8}\mid 0,-mx,0),(\frac{1}{8},x,\frac{1}{8}\mid -mx,0,0),(\frac{5}{8},\frac{3}{4} - x,\frac{1}{8}\mid mx,0,0),(\frac{1}{8},\frac{1}{8},x\mid 0,0,-mx),(\frac{1}{8},\frac{5}{8},\frac{3}{4} - x\mid 0,0,mx),(\frac{7}{8},x + \frac{1}{4},\frac{3}{8}\mid mx,0,0),(\frac{7}{8},-x,\frac{7}{8}\mid -mx,0,0),(x + \frac{3}{4},\frac{3}{8},\frac{3}{8}\mid 0,-mx,0),(\frac{1}{2} - x,\frac{7}{8},\frac{3}{8}\mid 0,mx,0),(\frac{7}{8},\frac{3}{8},\frac{1}{2} - x\mid 0,0,-mx),(\frac{3}{8},\frac{3}{8},x + \frac{3}{4}\mid 0,0,mx)$
32e $(x,x,x\mid \sqrt{3} mx/3,-\sqrt{3} mx/3,\sqrt{3} mx/3),(\frac{3}{4} - x,\frac{1}{4} - x,x + \frac{1}{2}\mid -\sqrt{3} mx/3,\sqrt{3} mx/3,\sqrt{3} mx/3),(\frac{1}{4} - x,x + \frac{1}{2},\frac{3}{4} - x\mid \sqrt{3} mx/3,\sqrt{3} mx/3,-\sqrt{3} mx/3),(x + \frac{1}{2},\frac{3}{4} - x,\frac{1}{4} - x\mid -\sqrt{3} mx/3,-\sqrt{3} mx/3,-\sqrt{3} mx/3),(x + \frac{3}{4},x + \frac{1}{4},\frac{1}{2} - x\mid -\sqrt{3} mx/3,\sqrt{3} mx/3,\sqrt{3} mx/3),(-x,-x,-x\mid \sqrt{3} mx/3,-\sqrt{3} mx/3,\sqrt{3} mx/3),(x + \frac{1}{4},\frac{1}{2} - x,x + \frac{3}{4}\mid \sqrt{3} mx/3,\sqrt{3} mx/3,-\sqrt{3} mx/3),(\frac{1}{2} - x,x + \frac{3}{4},x + \frac{1}{4}\mid -\sqrt{3} mx/3,-\sqrt{3} mx/3,-\sqrt{3} mx/3)$
16d $(\frac{1}{2},\frac{1}{2},\frac{1}{2}\mid \sqrt{3} mx/3,-\sqrt{3} mx/3,\sqrt{3} mx/3),(\frac{1}{4},\frac{3}{4},0\mid -\sqrt{3} mx/3,\sqrt{3} mx/3,\sqrt{3} mx/3),(\frac{3}{4},0,\frac{1}{4}\mid \sqrt{3} mx/3,\sqrt{3} mx/3,-\sqrt{3} mx/3),(0,\frac{1}{4},\frac{3}{4}\mid -\sqrt{3} mx/3,-\sqrt{3} mx/3,-\sqrt{3} mx/3)$
16c $(0,0,0\mid \sqrt{3} mx/3,-\sqrt{3} mx/3,\sqrt{3} mx/3),(\frac{3}{4},\frac{1}{4},\frac{1}{2}\mid -\sqrt{3} mx/3,\sqrt{3} mx/3,\sqrt{3} mx/3),(\frac{1}{4},\frac{1}{2},\frac{3}{4}\mid \sqrt{3} mx/3,\sqrt{3} mx/3,-\sqrt{3} mx/3),(\frac{1}{2},\frac{3}{4},\frac{1}{4}\mid -\sqrt{3} mx/3,-\sqrt{3} mx/3,-\sqrt{3} mx/3)$
8b $(\frac{3}{8},\frac{3}{8},\frac{3}{8}\mid 0,0,0),(\frac{1}{8},\frac{5}{8},\frac{1}{8}\mid 0,0,0)$
8a $(\frac{1}{8},\frac{1}{8},\frac{1}{8}\mid 0,0,0),(\frac{7}{8},\frac{3}{8},\frac{3}{8}\mid 0,0,0)$
Site symmetry: $^{1}1$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $..^{m_{\!-\!101}}2$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
191 $\left\{m_{-101}||2_{01-1}|0 0 0\right\}$ $(-x,-z,-y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & -1 & 0 & 0\end{array}\right]$$
Site symmetry: $..^{m_{110}}m$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
113 $\left\{m_{110}||m_{1-10}|0 0 0\right\}$ $(y,x,z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
Site symmetry: $^{2_{010}}2.^{m_{\!-\!101}}m ^{m_{101}}m$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
50 $\left\{2_{010}||2_{100}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(x,\frac{1}{4} - y,\frac{1}{4} - z,+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{4}\end{array}\right]$$
89 $\left\{m_{101}||m_{011}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(x,\frac{1}{4} - z,\frac{1}{4} - y,-1,-w,v,-u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & 1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{1}{4}\end{array}\right]$$
182 $\left\{m_{-101}||m_{01-1}|0 0 0\right\}$ $(x,z,y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0\end{array}\right]$$
Site symmetry: $.^{3^{2}_{\!-\!11\!-\!1}}3^{m_{011}}m$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
18 $\left\{3^{1}_{-11-1}||3^{2}_{111}|0 0 0\right\}$ $(y,z,x,+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$
58 $\left\{3^{2}_{-11-1}||3^{1}_{111}|0 0 0\right\}$ $(z,x,y,+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0\end{array}\right]$$
113 $\left\{m_{110}||m_{1-10}|0 0 0\right\}$ $(y,x,z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
137 $\left\{m_{011}||m_{-101}|0 0 0\right\}$ $(z,y,x,-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$
182 $\left\{m_{-101}||m_{01-1}|0 0 0\right\}$ $(x,z,y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0\end{array}\right]$$
Site symmetry: $.^{3^{2}_{\!-\!11\!-\!1}}\!-\!3^{m_{011}}m$
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 $\left\{3^{2}_{-11-1}||-3^{1}_{111}|0 0 0\right\}$ $(-z,-x,-y,+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0\end{array}\right]$$
18 $\left\{3^{1}_{-11-1}||3^{2}_{111}|0 0 0\right\}$ $(y,z,x,+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$
32 $\left\{1||-1|0 0 0\right\}$ $(-x,-y,-z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
58 $\left\{3^{2}_{-11-1}||3^{1}_{111}|0 0 0\right\}$ $(z,x,y,+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0\end{array}\right]$$
72 $\left\{3^{1}_{-11-1}||-3^{2}_{111}|0 0 0\right\}$ $(-y,-z,-x,+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ -1 & 0 & 0 & 0\end{array}\right]$$
112 $\left\{m_{011}||2_{-101}|0 0 0\right\}$ $(-z,-y,-x,-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & 0 \\ 0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0\end{array}\right]$$
113 $\left\{m_{110}||m_{1-10}|0 0 0\right\}$ $(y,x,z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
137 $\left\{m_{011}||m_{-101}|0 0 0\right\}$ $(z,y,x,-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$
139 $\left\{m_{110}||2_{1-10}|0 0 0\right\}$ $(-y,-x,-z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
182 $\left\{m_{-101}||m_{01-1}|0 0 0\right\}$ $(x,z,y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0\end{array}\right]$$
191 $\left\{m_{-101}||2_{01-1}|0 0 0\right\}$ $(-x,-z,-y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & -1 & 0 & 0\end{array}\right]$$
Site symmetry: $.^{3^{2}_{\!-\!11\!-\!1}}\!-\!3^{m_{011}}m$
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 $\left\{3^{2}_{-11-1}||-3^{1}_{111}|0 0 0\right\}$ $(-z,-x,-y,+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0\end{array}\right]$$
18 $\left\{3^{1}_{-11-1}||3^{2}_{111}|0 0 0\right\}$ $(y,z,x,+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$
32 $\left\{1||-1|0 0 0\right\}$ $(-x,-y,-z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
58 $\left\{3^{2}_{-11-1}||3^{1}_{111}|0 0 0\right\}$ $(z,x,y,+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0\end{array}\right]$$
72 $\left\{3^{1}_{-11-1}||-3^{2}_{111}|0 0 0\right\}$ $(-y,-z,-x,+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ -1 & 0 & 0 & 0\end{array}\right]$$
112 $\left\{m_{011}||2_{-101}|0 0 0\right\}$ $(-z,-y,-x,-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & 0 \\ 0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0\end{array}\right]$$
113 $\left\{m_{110}||m_{1-10}|0 0 0\right\}$ $(y,x,z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
137 $\left\{m_{011}||m_{-101}|0 0 0\right\}$ $(z,y,x,-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$
139 $\left\{m_{110}||2_{1-10}|0 0 0\right\}$ $(-y,-x,-z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0\end{array}\right]$$
182 $\left\{m_{-101}||m_{01-1}|0 0 0\right\}$ $(x,z,y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0\end{array}\right]$$
191 $\left\{m_{-101}||2_{01-1}|0 0 0\right\}$ $(-x,-z,-y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & -1 & 0 & 0\end{array}\right]$$
Site symmetry: $^{\!-\!4^{3}_{010}}\!-\!4^{3^{2}_{\!-\!11\!-\!1}}3^{m_{1\!-\!10}}m$
op_index Seitz coordinate spin_expr space_expr
1 $\left\{1||1|0 0 0\right\}$ $(x,y,z,+1,u,v,w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
18 $\left\{3^{1}_{-11-1}||3^{2}_{111}|0 0 0\right\}$ $(y,z,x,+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$
23 $\left\{-4^{1}_{100}||-4^{1}_{010}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(\frac{3}{4} - z,\frac{3}{4} - y,x,-1,-u,w,-v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{3}{4} \\ 1 & 0 & 0 & 0\end{array}\right]$$
25 $\left\{3^{2}_{1-1-1}||3^{1}_{-1-11}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(\frac{3}{4} - z,x,\frac{3}{4} - y,+1,-v,w,-u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & 1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{3}{4} \\ 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{3}{4}\end{array}\right]$$
49 $\left\{-4^{3}_{001}||-4^{3}_{001}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(\frac{3}{4} - y,x,\frac{3}{4} - z,-1,-v,u,-w)$ $$\begin{bmatrix}0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{3}{4} \\ 1 & 0 & 0 & 0 \\ 0 & 0 & -1 & \frac{3}{4}\end{array}\right]$$
51 $\left\{2_{010}||2_{100}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(x,\frac{3}{4} - y,\frac{3}{4} - z,+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{3}{4}\end{array}\right]$$
58 $\left\{3^{2}_{-11-1}||3^{1}_{111}|0 0 0\right\}$ $(z,x,y,+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0\end{array}\right]$$
73 $\left\{3^{1}_{-1-11}||3^{2}_{-11-1}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(\frac{3}{4} - y,\frac{3}{4} - z,x,+1,-w,u,-v)$ $$\begin{bmatrix}0 & 0 & -1 \\ 1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{3}{4} \\ 1 & 0 & 0 & 0\end{array}\right]$$
83 $\left\{m_{101}||m_{011}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(x,\frac{3}{4} - z,\frac{3}{4} - y,-1,-w,v,-u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & 1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 0 & -1 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{3}{4}\end{array}\right]$$
88 $\left\{m_{1-10}||m_{110}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(\frac{3}{4} - y,\frac{3}{4} - x,z,-1,v,u,w)$ $$\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & 0\end{array}\right]$$
101 $\left\{-4^{3}_{010}||-4^{1}_{100}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(\frac{3}{4} - x,z,\frac{3}{4} - y,-1,w,-v,-u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & 0 \\ 0 & -1 & 0 & \frac{3}{4}\end{array}\right]$$
113 $\left\{m_{110}||m_{1-10}|0 0 0\right\}$ $(y,x,z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
117 $\left\{-4^{1}_{001}||-4^{1}_{001}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(y,\frac{3}{4} - x,\frac{3}{4} - z,-1,v,-u,-w)$ $$\begin{bmatrix}0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ -1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{3}{4}\end{array}\right]$$
120 $\left\{-4^{1}_{010}||-4^{3}_{100}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(\frac{3}{4} - x,\frac{3}{4} - z,y,-1,-w,-v,u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & -1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{4} \\ 0 & 0 & -1 & \frac{3}{4} \\ 0 & 1 & 0 & 0\end{array}\right]$$
121 $\left\{2_{100}||2_{010}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(\frac{3}{4} - x,y,\frac{3}{4} - z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{4} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{3}{4}\end{array}\right]$$
127 $\left\{m_{01-1}||m_{101}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(\frac{3}{4} - z,y,\frac{3}{4} - x,-1,u,w,v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{3}{4} \\ 0 & 1 & 0 & 0 \\ -1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
130 $\left\{3^{1}_{1-1-1}||3^{2}_{-1-11}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(y,\frac{3}{4} - z,\frac{3}{4} - x,+1,-w,-u,v)$ $$\begin{bmatrix}0 & 0 & -1 \\ -1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
137 $\left\{m_{011}||m_{-101}|0 0 0\right\}$ $(z,y,x,-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$
142 $\left\{3^{1}_{111}||3^{2}_{1-1-1}|\frac{3}{4} 0 \frac{3}{4}\right\}$ $(\frac{3}{4} - y,z,\frac{3}{4} - x,+1,w,u,v)$ $$\begin{bmatrix}0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & 0 \\ -1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
143 $\left\{3^{2}_{-1-11}||3^{1}_{-11-1}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(z,\frac{3}{4} - x,\frac{3}{4} - y,+1,v,-w,-u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & -1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ -1 & 0 & 0 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{3}{4}\end{array}\right]$$
153 $\left\{-4^{3}_{100}||-4^{3}_{010}|0 \frac{3}{4} \frac{3}{4}\right\}$ $(z,\frac{3}{4} - y,\frac{3}{4} - x,-1,-u,-w,v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 0 & -1 & 0 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{3}{4}\end{array}\right]$$
169 $\left\{2_{001}||2_{001}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(\frac{3}{4} - x,\frac{3}{4} - y,z,+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{3}{4} \\ 0 & -1 & 0 & \frac{3}{4} \\ 0 & 0 & 1 & 0\end{array}\right]$$
182 $\left\{m_{-101}||m_{01-1}|0 0 0\right\}$ $(x,z,y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0\end{array}\right]$$
186 $\left\{3^{2}_{111}||3^{1}_{1-1-1}|\frac{3}{4} \frac{3}{4} 0\right\}$ $(\frac{3}{4} - z,\frac{3}{4} - x,y,+1,v,w,u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{3}{4} \\ -1 & 0 & 0 & \frac{3}{4} \\ 0 & 1 & 0 & 0\end{array}\right]$$
Site symmetry: $^{\!-\!4^{3}_{010}}\!-\!4^{3^{2}_{\!-\!11\!-\!1}}3^{m_{1\!-\!10}}m$
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 $\left\{m_{1-10}||m_{110}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(\frac{1}{4} - y,\frac{1}{4} - x,z,-1,v,u,w)$ $$\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & 0\end{array}\right]$$
18 $\left\{3^{1}_{-11-1}||3^{2}_{111}|0 0 0\right\}$ $(y,z,x,+1,w,-u,-v)$ $$\begin{bmatrix}0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$
24 $\left\{3^{2}_{1-1-1}||3^{1}_{-1-11}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(\frac{1}{4} - z,x,\frac{1}{4} - y,+1,-v,w,-u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & 1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{4} \\ 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{1}{4}\end{array}\right]$$
42 $\left\{-4^{3}_{010}||-4^{1}_{100}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(\frac{1}{4} - x,z,\frac{1}{4} - y,-1,w,-v,-u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & 0 \\ 0 & -1 & 0 & \frac{1}{4}\end{array}\right]$$
50 $\left\{2_{010}||2_{100}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(x,\frac{1}{4} - y,\frac{1}{4} - z,+1,-u,v,-w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & -1 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{4}\end{array}\right]$$
58 $\left\{3^{2}_{-11-1}||3^{1}_{111}|0 0 0\right\}$ $(z,x,y,+1,-v,-w,u)$ $$\begin{bmatrix}0 & -1 & 0 \\ 0 & 0 & -1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0\end{array}\right]$$
68 $\left\{-4^{3}_{100}||-4^{3}_{010}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(z,\frac{1}{4} - y,\frac{1}{4} - x,-1,-u,-w,v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 0 & -1 & 0 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
84 $\left\{3^{1}_{-1-11}||3^{2}_{-11-1}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(\frac{1}{4} - y,\frac{1}{4} - z,x,+1,-w,u,-v)$ $$\begin{bmatrix}0 & 0 & -1 \\ 1 & 0 & 0 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{4} \\ 1 & 0 & 0 & 0\end{array}\right]$$
89 $\left\{m_{101}||m_{011}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(x,\frac{1}{4} - z,\frac{1}{4} - y,-1,-w,v,-u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & 1 & 0 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{1}{4}\end{array}\right]$$
102 $\left\{-4^{1}_{100}||-4^{1}_{010}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(\frac{1}{4} - z,\frac{1}{4} - y,x,-1,-u,w,-v)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{1}{4} \\ 1 & 0 & 0 & 0\end{array}\right]$$
113 $\left\{m_{110}||m_{1-10}|0 0 0\right\}$ $(y,x,z,-1,-v,-u,w)$ $$\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]$$
116 $\left\{2_{100}||2_{010}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(\frac{1}{4} - x,y,\frac{1}{4} - z,+1,u,-v,-w)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{4} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{4}\end{array}\right]$$
119 $\left\{-4^{1}_{001}||-4^{1}_{001}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(y,\frac{1}{4} - x,\frac{1}{4} - z,-1,v,-u,-w)$ $$\begin{bmatrix}0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ -1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{4}\end{array}\right]$$
125 $\left\{3^{1}_{1-1-1}||3^{2}_{-1-11}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(y,\frac{1}{4} - z,\frac{1}{4} - x,+1,-w,-u,v)$ $$\begin{bmatrix}0 & 0 & -1 \\ -1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 1 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
126 $\left\{-4^{1}_{010}||-4^{3}_{100}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(\frac{1}{4} - x,\frac{1}{4} - z,y,-1,-w,-v,u)$ $$\begin{bmatrix}0 & 0 & -1 \\ 0 & -1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{4} \\ 0 & 0 & -1 & \frac{1}{4} \\ 0 & 1 & 0 & 0\end{array}\right]$$
136 $\left\{3^{2}_{-1-11}||3^{1}_{-11-1}|0 \frac{1}{4} \frac{1}{4}\right\}$ $(z,\frac{1}{4} - x,\frac{1}{4} - y,+1,v,-w,-u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & -1 \\ -1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ -1 & 0 & 0 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{1}{4}\end{array}\right]$$
137 $\left\{m_{011}||m_{-101}|0 0 0\right\}$ $(z,y,x,-1,u,-w,-v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$
152 $\left\{-4^{3}_{001}||-4^{3}_{001}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(\frac{1}{4} - y,x,\frac{1}{4} - z,-1,-v,u,-w)$ $$\begin{bmatrix}0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{4} \\ 1 & 0 & 0 & 0 \\ 0 & 0 & -1 & \frac{1}{4}\end{array}\right]$$
154 $\left\{3^{1}_{111}||3^{2}_{1-1-1}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(\frac{1}{4} - y,z,\frac{1}{4} - x,+1,w,u,v)$ $$\begin{bmatrix}0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & -1 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & 0 \\ -1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
156 $\left\{m_{01-1}||m_{101}|\frac{1}{4} 0 \frac{1}{4}\right\}$ $(\frac{1}{4} - z,y,\frac{1}{4} - x,-1,u,w,v)$ $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{4} \\ 0 & 1 & 0 & 0 \\ -1 & 0 & 0 & \frac{1}{4}\end{array}\right]$$
170 $\left\{2_{001}||2_{001}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(\frac{1}{4} - x,\frac{1}{4} - y,z,+1,-u,-v,w)$ $$\begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}-1 & 0 & 0 & \frac{1}{4} \\ 0 & -1 & 0 & \frac{1}{4} \\ 0 & 0 & 1 & 0\end{array}\right]$$
182 $\left\{m_{-101}||m_{01-1}|0 0 0\right\}$ $(x,z,y,-1,w,v,u)$ $$\begin{bmatrix}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0\end{array}\right]$$
184 $\left\{3^{2}_{111}||3^{1}_{1-1-1}|\frac{1}{4} \frac{1}{4} 0\right\}$ $(\frac{1}{4} - z,\frac{1}{4} - x,y,+1,v,w,u)$ $$\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}$$ $$\left[\begin{array}{ccc|c}0 & 0 & -1 & \frac{1}{4} \\ -1 & 0 & 0 & \frac{1}{4} \\ 0 & 1 & 0 & 0\end{array}\right]$$