If this were purely theoretical, the contact point would be one atom wide. Whatever the materials are, if there is a contact point between them, and they don't "go through" each other, then at least one atom from the ball and one atom from the base would need to be in contact each other. Actually it would only be the Valence electrons on the outer rings of each of the two atoms that would be repelling each other, giving the illusion of contact.
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