3. From the edges and the diagonals on the faces of a cube, select $k$ lines such that any two of these lines are skew lines. Then the maximum value of $k$ is . $\qquad$
4
3.【Analysis and Solution】It examines 4 line segments $A C, B C_{1}, D_{1} B_{1}, A_{1} D$, where the lines they lie on are pairwise skew lines. If there are 5 or more line segments that meet the conditions, their endpoints would be distinct and no fewer than 10, but the cube has only 8 vertices, which is a contradiction. Therefore, the maximum value of $k$ is 4.