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this depends on the input quite a bit. Namely, the following factors play a big role:

  • how many facets your polytope $P$ has
  • how big in abs. value the coordinates of your points are (assuming they are all integers)
  • how degenerate $P$ is; i.e. the maximal number of neighbours of a vertex of $P$ --- the more degenerate it is, the slower the facet enumeration)