$D_6\otimes F_2$
$${\rm LOG}\left(D_6 \otimes F_2\right)=\frac{1}{2}\pi
\left[\begin{array}{rrrrrrrrrrrr}
\bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet\\
\bullet & 2 & \bullet & 2 & \bullet & 2 & \bullet & 2 & \bullet & 2 & \bullet & 2\\
\bullet & \bullet & 2 & 2 & 1 & 1 & 3 & 3 & 3 & 3 & 1 & 1\\
\bullet & 2 & 2 & \bullet & 1 & 3 & 3 & 1 & 3 & 1 & 1 & 3\\
\bullet & \bullet & 1 & 1 & 2 & 2 & 1 & 1 & 3 & 3 & 3 & 3\\
\bullet & 2 & 1 & 3 & 2 & \bullet & 1 & 3 & 3 & 1 & 3 & 1\\
\bullet & \bullet & 3 & 3 & 1 & 1 & 2 & 2 & 1 & 1 & 3 & 3\\
\bullet & 2 & 3 & 1 & 1 & 3 & 2 & \bullet & 1 & 3 & 3 & 1\\
\bullet & \bullet & 3 & 3 & 3 & 3 & 1 & 1 & 2 & 2 & 1 & 1\\
\bullet & 2 & 3 & 1 & 3 & 1 & 1 & 3 & 2 & \bullet & 1 & 3\\
\bullet & \bullet & 1 & 1 & 3 & 3 & 3 & 3 & 1 & 1 & 2 & 2\\
\bullet & 2 & 1 & 3 & 3 & 1 & 3 & 1 & 1 & 3 & 2 & \bullet
\end{array}\right]$$