On the blocking numbers of some special convex bodies

Abstract

In this paper, we study the blocking numbers of some special convex bodies. We determine the exact blocking number of a rhombic dodecahedra and a $3$-dimensional cylinder $H$ whose base is a $2$-dimensional convex domain. We also estimate that the blocking number of the $\ell_{p}$ unit ball in $\mathbb{E}^{3}$ is at most $6$, for $1\leq p<+\infty$. In high dimensions, the blocking number of the $\ell_{p}$ unit ball in $\mathbb{E}^{d}$ is at most $2d$, for $\log_{2}d<p<+\infty$.