Projective Equivalences of k-neighbourly Polytopes

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