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On the reconstruction of polytopes
[article]
2018
arXiv
pre-print
Blind and Mani, and later Kalai, showed that the face lattice of a simple polytope is determined by its graph, namely its 1-skeleton. Call a vertex of a d-polytope nonsimple if the number of edges incident to it is more than d. We show that (1) the face lattice of any d-polytope with at most two nonsimple vertices is determined by its 1-skeleton; (2) the face lattice of any d-polytope with at most d-2 nonsimple vertices is determined by its 2-skeleton; and (3) for any d>3 there are two
arXiv:1702.08739v4
fatcat:sihsekewqvcrtnyl4olxo4hmnq