> I'm sure that's what he means. In simple terms, there's no corner where > spaces touch diagonally. Spaces have an edge in common, or they don't touch > at all. > > If you want to get a little more detailed, you can prove that there can't be > any corner-touching if there's no place where more than three spaces come > together. And with hexes, they don't.
another way to think of it: a winning position allows you to build a highway as wide as the edge of a hexagon and drive all the way from one side to the other. if you cannot drive all the way, you dont win and the other guy can drive all the way on his hexagons.
on a checkerboard, the diagonals pinch your car into a singularity.