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I believe that is still a theoretical question as you would need to have infinite magnification to see what was really happening on an atomic level or even smaller level. Both corners, black/black AND white/white could never touch because the touching of two would electively block the potential for touching of the other two. However, I would then not consider this a perfect checkerboard pattern. Which leads me to believe the following: The place where the four corners get close is represented by the atoms of coloring or what ever substance makes up the squares these atoms and their electron clouds are at this point better represented by circles so you have. OO OO Which no matter how close you push them together there is that diamond shape of space in the middle keeping the diagonal opposites apart. But who knows maybe as our science gets better, or we find someone who knows science better will have a better understanding.
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