Consider an $n$-dimensional convex polytope with $k$ vertices. In the worst case the number of faces is exponential in $n$ and $k$. Consider a $2$-dimensional plane which intersects this polytope, i.e., it intersects only a subset of all faces. Can I bound the number of such intersected faces? In the worst case, will this number be a polynomial in $n$ and $k$ or still exponential?


Thanks in advance.



Section of an $n$-dimensional convex polytope by $2$-dimensional plane
I found a paper wich shows that in the worst case it still can be exponential:
"Shadows and slices of polytopes, Nina Amenta et al., 1996"
<https://dl.acm.org/citation.cfm?id=237228>


