9 research outputs found

    Cutting a polytope

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    We investigate whether it is the case that for every convex d -polytope P and pair of distinct vertices x and y of P , there exists a hyperplane passing through x and y which cuts P into two smaller d -polytopes, one of which has fewer facets than P . Such a result would lead to inductive proofs of Conjectures 1 and 2 below. However, for d ≥4, our answer is in the negative.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42814/1/10711_2005_Article_BF01265345.pd
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