$S_6\otimes F_2$
$${\rm LOG}\left(S_6 \otimes F_2\right)=\frac{1}{3}\pi
\left[\begin{array}{rrrrrrrrrrrr}
\bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet\\
\bullet & 3& \bullet& 3& \bullet & 3& \bullet& 3& \bullet & 3 & \bullet & 3\\
\bullet & \bullet & \bullet & \bullet & 2 & 2 & 2 & 2 & 4 & 4 & 4 & 4\\
\bullet & 3& \bullet& 3& 2& 5& 2& 5& 4& 1& 4& 1\\
\bullet & \bullet& 2& 2& \bullet& \bullet& 4& 4& 4& 4& 2& 2\\
\bullet & 3& 2& 5& \bullet& 3& 4& 1& 4& 1& 2& 5\\
\bullet & \bullet& 2& 2& 4& 4& \bullet& \bullet& 2& 2& 4& 4\\
\bullet & 3& 2& 5& 4& 1& \bullet& 3& 2& 5& 4& 1\\
\bullet & \bullet& 4& 4& 4& 4& 2& 2& \bullet& \bullet& 2& 2\\
\bullet & 3& 4& 1& 4& 1& 2& 5& \bullet& 3& 2& 5\\
\bullet & \bullet& 4& 4& 2& 2& 4& 4& 2& 2& \bullet& \bullet\\
\bullet & 3& 4& 1& 2& 5& 4& 1& 2& 5& \bullet& 3
\end{array}\right]$$