What do the new logic button Bounds?

I would like to know what is the function of the of the Button Bounds in the Logic Menu (F4) and of the Menu Button at its side.

As far as I can tell, the “Bounds” button lets you specify alternate Bounding Boxes for your objects in the game engine. Set it to “Box” for cubes, “Sphere” for spheres, etc. As for “Polyhedr” and “Polytope”, they let the shape of the object affect its physics. Here is an example: create a new scene with a fairly large plane on the origin. Add the “monkey” mesh, and set it a few units above the plane. Now, go into the "Logic’ menu and make your “monkey” a dynamic actor with rigid physics. Set your bounds to Polyhedr, then activate a test of your “game”. See what happens.