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My understanding is that convex hull of n points in 4D could have O(n²) edges in the worst case. Source: https://sites.cs.ucsb.edu/~suri/cs235/ConvexHull.pdf This same source writes In 4D, there are ...

Given a set of $n$ points in $\mathbb{R}^d$, is there an algorithm to determine if the convex hull contains the unit ball centered at the origin in polynomial time (in both $n$ and $d$)? The convex ...