Projective Equivalences of k-neighbourly Polytopes

Abstract

We prove the following theorem, which is related to McMullen's problem on projective transformations of polytopes; let $2\le k\le \lfloor \frac{d}{2}\rfloor$ 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 $d+\lceil \frac{d}{k}\rceil +1\le \nu (d,k)<2d-k+1$.

arXiv commentSubmitted to Contributions to Discrete Mathematics