2 problems

Let $\Lambda_1=\frac{2}{\sqrt{3}}\mathsf{A}_2$ be the triangular lattice in dimension $2$, and let $\Lambda$ have the shape of $\mathsf{D}_3$, $\mathsf{D}_4$, $\mathsf{E}_8$, or…

Let $d\in\{2,3,4,8,24\}$ and let $\Lambda$ be respectively $\Lambda_1$, $\mathsf{D}_3$, $\mathsf{D}_4$, $\mathsf{E}_8$, or $\Lambda_{24}$. For $x_2>x_1>d$, let $E_f$ be the Lennard…