TITLE: Section of an $n$-dimensional convex polytope by $2$-dimensional plane
QUESTION [7 upvotes]: 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.

REPLY [2 votes]: 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