$S_6$
$${\rm LOG}\left(S_6\right)=\frac{2}{3}\pi
\left[\begin{array}{rrrrrr}
\bullet & \bullet & \bullet & \bullet & \bullet & \bullet\\
\bullet & \bullet & 1 & 1 & 2 & 2\\
\bullet & 1 & \bullet & 2 & 2 & 1\\
\bullet & 1 & 2 & \bullet & 1 & 2\\
\bullet & 2 & 2 & 1 & \bullet & 1\\
\bullet & 2 & 1 & 2 & 1 & \bullet
\end{array}\right]$$