$X_{12}$
$${\rm LOG}\left(X_{12}\right)=\frac{2}{3}\pi
\left[\begin{array}{rrrrrrrrrrrr}
\bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet\\
\bullet &\bullet & \bullet & \bullet & 1 & 1 & 1 & 1 & 2 & 2 & 2 & 2\\
\bullet &\bullet & \bullet & 1 & \bullet & 2 & 2 & 2 & 1 & 1 & 1 & 2\\
\bullet &\bullet & 1 & 2 & 2 & \bullet & 1 & 2 & \bullet & 1 & 2 & 1\\
\bullet &1 & \bullet & 2 & 2 & 1 & 2 & \bullet & 2 & \bullet & 1 & 1\\
\bullet &1 & 2 & \bullet & 1 & 2 & \bullet & 2 & \bullet & 2 & 1 & 1\\
\bullet &1 & 2 & 1 & 2 & \bullet & \bullet & 1 & 2 & 1 & \bullet & 2\\
\bullet &1 & 2 & 2 & \bullet & 2 & 1 & 1 & 1 & \bullet & 2 & \bullet\\
\bullet &2 & 1 & \bullet & 2 & \bullet & 2 & 1 & 1 & 2 & 1 & \bullet\\
\bullet &2 & 1 & 1 & \bullet & 2 & 1 & \bullet & 2 & 2 & \bullet & 1\\
\bullet &2 & 1 & 2 & 1 & 1 & \bullet & 2 & 1 & \bullet & \bullet & 2\\
\bullet &2 & 2 & 1 & 1 & 1 & 2 & \bullet & \bullet & 1 & 2 & \bullet
\end{array}\right]$$
Found by T. Banica and J.-M. Schlenker [1].