Question

Consider a cube of side length 3. We form a new polyhedron by cutting out a cube of side length 1 from each of the 8 corners of the original cube. Let this new polyhedron have f faces, e edges and v vertices. What is the value of f+e+v?

Answer 1

3 extra faces for each corner: f = 6 + 3 * 8 = 30
9 extra edges for each corner: e = 12 + 9 * 8 = 84
each vertex is replaced by 7 vertices: v = 7 * 8 = 56
for a grand total of f+e+v = 170

Answer 2

I did all the same but couldn't imagine edges , why 9 extra?

Answer 3

when in doubt, draw it out

Answer 4

I tried in mind, so made mistake in edge counting... thank u .