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 $ν{(d, k)}$ be the largest number such that any set of $ν{(d,k)}$ 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 $d + \left\lceil{\frac{d}{k}}\right\rceil +1 \leq ν{(d, k)} < 2d-k +1$.

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