$F_5$

$${\rm LOG}\left(F_5\right)=\frac{2}{5}\pi \left[\begin{array}{rrrrr} \bullet & \bullet & \bullet & \bullet & \bullet\\ \bullet & 1 & 2 & 3 & 4\\ \bullet & 2 & 4 & 1 & 3\\ \bullet & 3 & 1 & 4 & 2\\ \bullet & 4 & 3 & 2 & 1 \end{array}\right]$$