# Edge-Ploding Polyhedra

Geometry Level 3

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):

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