Distinct planes $p_1,p_2,\dots ,p_k$ intersect the interior of a cube $Q$. Let $S$ be the union of the faces of $Q$ and let $P={\bigcup }_{j=1}^k{p}_j$. The intersection of $P$ and $S$ consists of the union of all segments joining the midpoints of every pair of $\text{opposite}$ edges belonging to the same face of $Q$. What is the difference between the maximum and minimum possible values of $k$?