Edge-Ploding Polyhedra

Geometry Level 1

Let PP be a polyhedron that is the convex hull of the vertices v1,v2,,vnv_1, v_2, \ldots , v_n and with edges e1,e2,,em 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 vi,vj v_i, v_j .

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

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






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