We study the problem of partitioning point sets in the space so that each equivalence class is a convex polytope disjoint from the others. For a set of n points P in R 3 , define f( P) to be the minimum number of sets in a partition into disjoint convex polytopes of P and F( n) as the maximum of f( P), over all sets P of n points. We show that ⌈ n/2(log 2 n+1)⌉≤ F( n)≤⌈2 n/9⌉. The lower bound also holds for partition into empty convex polytopes.