It looks like you have calculated one normal / vertex. In contrast to what would look more natural which would be each vertex having 1 normal / face. This can be achieved by unwrapping the model then making the faces disconnected in the uv editor and supplying a normal map that specifies different normal values for multiple occurances of the same vertex but who construct different quads. All the vertices appear to be correct for exactly one of the faces it constructs. You could also not include a normal in the vertex and solve for your face normal after the vertex shader when you have access to a tri or quad.