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 $d + \left\lceil{ \frac{ d}{ k}}\right\rceil +1 \leq \nu{ (d, k)} < 2d-k +1$.
Categories: math.CO