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2 Facet Enumeration

Input: Polytope P in V-description with n points
Output: Non-redundant H-description of P
Status (general): Open; polynomial total time if P is simple or simplicial
Status (fixed dim.): Polynomial time
In [1] it is shown that FACET ENUMERATION is strongly polynomially equivalent to Problem 3 and thus to Problem 1 (see the comments there).

For this problem, one can assume to have an interior point (e.g., the vertex barycenter). FACET ENUMERATION is sometimes called the convex hull problem.