Combinatorial Polytope Enumeration
نویسندگان
چکیده
We describe a provably complete algorithm for the generation of a tight, possibly exact, superset of all combinatorially distinct simple n-facet polytopes in Rd, along with their graphs, f -vectors, and face lattices. The technique applies repeated cutting planes and planar sweeps to a d−simplex. Our generator has implications for several outstanding problems in polytope theory, including conjectures about the number of distinct polytopes, the edge expansion of polytopal graphs, and the d-step conjecture.
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تاریخ انتشار 2009