Each one of the faces has 20 vertices (I know that every face is actually made out of triangles), but shouldn't it have the same normals? Or maybe there is a way to access those "background virtual faces" and fix it? It also does show up in the render.
I've noticed that it only happens with smooth shading. (Isn't it supposed to make things smoother?) I think it's okay with just flat shading, but I still want to know what's up.
Edge split modifier seems to be a good solution.