Minimum Energy Configuration of Particles with Six-Fold Rotational Symmetry

The output configuration resulting from the minimization of a system of 800 particles driven by the Lennard-Jones potential, with parameters: $\sigma = 0.95589..$ and $\epsilon = \frac{1}{4}$

$\begin{equation*} E_{LJ}=\frac{1}{2}\sum_{a \in A} \sum_{b \in B} 4\epsilon\left[\left(\frac{\sigma}{r_{ab}}\right)^{12} - \left(\frac{\sigma}{r_{ab}}\right)^{6}\right] \end{equation*}$