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 . $\qquad$
3. Consider the 4 line segments $A C$, $B C_{1}$, $D_{1} B_{1}$, $A_{1} D$, the lines on which they lie are pairwise skew lines. If there are 5 or more such line segments, then their endpoints are distinct and there are at least 10, but a cube has only 8 vertices, which is a contradiction. Therefore, the maximum value of $k$ is 4.