**A. Kharazishvili**

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

**abstract:**

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.