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has six facets. The Hirsch conjecture then indicates that the diameter of this cube cannot be greater than three. Accepting the conjecture would imply that any two vertices of the cube may be connected by a path from vertex to vertex using, at most, three steps. For all polytopes of dimension at least 8, this bound is actually optimal; no polytope of dimension has a diameter less than n-d, with n being the number of its facets, as before. In other words, for nearly all cases, the conjecture provides

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