Seeing is believing - just try:
1 -draw a square - add two vertices in the middle of the upper and lower sides - bend the surface on the (virtual) line connecting the new vertices by selecting and dragging both end vertices of the corresponding sides - say "ooooh"....
2 - now do the same but insert the new vertices in the right and left sides - say "what the heck???"
M. C. Escher would have loved it, but to me it looked more like a medium-heavy hangover
Can anyone offer a consistent theory on what happens to an originally plane surface having more than 3 vertices when some of them get displaced along the normal?