  We prove the following theorem, which is related to McMullen's problem on
projective transformations of polytopes; let $2\leq k\leq
\lfloor{\frac{d}{2}}\rfloor$ and $\nu{(d, k)}$ be the largest number such that
any set of $\nu{(d,k)}$ points lying in general position in $\mathbb{R}^d$ can
be mapped by a permissible projective transformation onto the vertices of a
k-neighborly polytope, then $d + \left\lceil{\frac{d}{k}}\right\rceil +1 \leq
\nu{(d, k)} < 2d-k +1$.
