We describe a new technique for constructing convex polytopes—a generalization of Shemer’s sewing construction for simplicial neighborly polytopes that has been modified to allow the creation of nonsimplicial polytopes as well. We show that Bisztriczky’s ordinary polytopes can be constructed in this manner, and we also construct several infinite families of polytopes. We consider bounds on the flag f-vectors of 4-polytopes that can be inductively constructed by generalized sewing starting from the 4-simplex.
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