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In 1957, Hadwiger made a conjecture that every $n$-dimensional convex bodycan be covered by $2^n$ translations of its interior. The Hadwiger's coveringfunctional $\gamma_m(K)$ is the smallest positive number $r$ such that $K$ canbe covered by $m$ translations of $rK$. Due to Zong's program, we study theHadwiger's covering functional for the simplex and the cross-polytope. In thispaper, we give upper bounds for the Hadwiger's covering functional of thesimplex and the cross-polytope.

On Hadwiger's covering functional for the simplex and the cross-polytope