Edge-Ploding Polyhedra

Let $P$ be a polyhedron that is the convex hull of the vertices $v_1, v_2, \ldots , v_n$ and with edges $e_1, e_2, \ldots , e_m$ where each edge is defined to be the set of points on the line that passes through some two distinct vertices $v_i, v_j$ .

We define the Edge-Plosion of $P$ , $E!( P )$ , to be the convex hull of the mid-points of each edge of $P$ , where $P$ is a cube.

Which of these is an image of $E!(E!(P))$ ?

(A) :

(B) :

(C) :

(D) :