Solution of Hadwiger-Levi's Covering Problem for Duals of Cyclic 2k-Polytopes

For a collection C of convex bodies let h(C) be the minimum number m with the property that every element K of C can be covered by m or fewer smaller homothetic copies of K. Denote by C_d^* the collection of all duals of cyclic d-polytopes, d 2. We show that h(C_2k^*)=(k +1)2 for any k 2. We also prove the inequalities (d+1) (d+3)/4 h(C_d^*) (d+1) 2/2$ for any d 2.