Suppose we have a 2D compact closed smooth surface in $\Bbb R^3$. And for any plane, there are at most 3 points on the surface tangent to it.
So the question is that can we classify the points on the surface into 3 sets $A, B, C$, which are pairwise disjoint and the union is the entire surface, such that every set is a connected set and any 2 points in the same set won't share a common tangent plane?