# Kuperberg, Greg

## Fat 4-polytopes ★★★

Author(s): Eppstein; Kuperberg; Ziegler

The \emph{fatness} of a 4-\Def{polytope} $P$ is defined to be $(f_1 + f_2)/(f_0 + f_3)$ where $f_i$ is the number of faces of $P$ of dimension $i$.

\begin{question} Does there exist a fixed constant $c$ so that every convex 4-polytope has fatness at most $c$? \end{question}

Keywords: f-vector; polytope