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Almost simplicial polytopes: the lower and upper bound theorems
journal contributionposted on 2020-04-01, 00:00 authored by Eran Nevo, Guillermo Pineda-Villavicencio, Julien UgonJulien Ugon, David Yost
We study -vertex -dimensional polytopes with at most one nonsimplex facet with, say, vertices, called almost simplicial polytopes. We provide tight lower and upper bound theorems for these polytopes as functions of , and , thus generalizing the classical Lower Bound Theorem by Barnette and the Upper Bound Theorem by McMullen, which treat the case where . We characterize the minimizers and provide examples of maximizers for any . Our construction of maximizers is a generalization of cyclic polytopes, based on a suitable variation of the moment curve, and is of independent interest.