Re: funny results
For more fun, perform a Surface -> Change Vertex Order and the "escher-effect" happens on the opposite selection.
4+ sided polys allow you to "break some rules" in 3D that should keep things like this from happening.
My 3D programming skills are a few years old, so anyone feel free to correct me if I'm off, but when the 6-sided shape is drawn on-screen, it is still drawn as triangles. When you pull the vertices at odd angles like this, the triangles being drawn will start to appear where you may not have expected them, based on the vertex ordering and the vertices you move.
Any time you push vertices like this, it's simply best to break the geometry up to form a crease along that section so you get consistent, predictable results.
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