3. A convex polyhedron $P$ with 2021 edges, after cutting off a pyramid at each vertex, results in a new convex polyhedron $Q$. The base planes of these cut-off pyramids do not intersect each other on or inside $P$. Then the number of edges of the convex polyhedron $Q$ is $\qquad$
3. 6063.

Notice that, all the edges of $P$ are still edges of $Q$, and the new edges in $Q$ are formed by the bases of the cut-off pyramids. The number of new edges added by each pyramid is equal to the number of edges emanating from its vertex. Therefore, $Q$ has $2021 + 2 \times 2021 = 6063$ edges.