A Vertex-Skipping property for almost-minimizers of the relative perimeter in convex sets

Given a convex domain $\mathrm{\Omega }\subset {\mathbb{R}}^3$ and an almost-minimizer $E$ of the relative perimeter in $\mathrm{\Omega }$, we prove that the closure of $\mathrm{\partial }E\cap \mathrm{\Omega }$ does not contain vertices of $\mathrm{\Omega }$.