4 problems

Let $\M$ be the model under consideration, let $F$ be a face of $\M$ of dimension $d-k$ for some $k\geq 2$, and let $G_1,\ldots,G_m$ be the faces of dimension $d-k+1$ containing…

Conway–Sloane's conjecture. The function $f$ characterizes $L$ up to conjugacy in every dimension; Conway and Sloane proved this in dimensions at most $3$.

Let $\mathsf{A}_n$ and $\mathsf{D}_n$ be the root lattices in their natural embeddings, and consider both the $L^1$ and $L^{\infty}$ polyhedral norms. Write $V_{<}(N_{\mathcal L})$…

Let $\Gamma$ be a graph. The Voronoi polyhedron of $\Gamma$ is … Let ${\rm Faces}({\rm Vor}_{\Gamma})$ be the poset of faces of ${\rm Vor}_{\Gamma}$, ordered by reverse inclusion,…