A. Kharazishvili

On Faces of a Convex Polyhedron in ${\bf R}^3$ with a Small Number of Sides

For any convex polyhedron $P \subset {\bf R}^3$ and for any natural number $k$, let $F_k(P)$ denote the number of all faces of $P$ with exactly $k$ sides. It is well known that $F_k(P) \geq 2$ for at least one $k$. We consider the question whether $F_k(P) \geq 3$, for at least one $k$, and present a solution to it. Some related questions are also discussed.