Let n ∈ N, and let Q n = [0,1] n . For a nondegenerate simplex S ⊂ R n , by σS we mean the homothetic copy of S with center of homothety in the center of gravity of S and ratio of homothety σ. Put ξ(S) = min{σ > 1 : Q n ⊂ σS}, ξ n = min{ξ(S) : S ⊂ Q n }.
