Projective Equivalences of k-neighbourly Polytopes

Let $$2\le k\le \left\lfloor {\frac{d}{2}}\right\rfloor $$2≤k≤d2 and let $$\nu {(d, k)}$$ν(d,k) be the largest number such that any set of $$\nu {(d,k)}$$ν(d,k) points lying in general position in $$\mathbb {R}^d$$Rd can be mapped by a permissible projective transformation onto the vertices of a k-neighborly polytope. The aim of this paper is to prove that $$d + \left\lceil { \frac{d}{k}}\right\rceil +1 \le \nu {(d, k)} < 2d-k +1$$d+dk+1≤ν(d,k)<2d-k+1.