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 \( E!(E!(P)) \)?






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