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22 Polytope Isomorphism

Input: The face lattices LP and LQ of two polytopes P and Q, respectively
Output: "Yes" if LP is isomorphic to LQ, "No" otherwise
Status (general): Open
Status (fixed dim.): Polynomial time
The problem can be solved in polynomial time in constant dimension (see Problem 23). In general, the problem can easily be reduced to the graph isomorphism problem