Distinct planes p_{1}, p_{2}, \ldots, 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 edges belonging to the same face of Q. What is the difference between the maximum and the minimum possible values of k ?
Answer Choices
A. 8
B. 12
C. 20
D. 23
E. 24