A note on Kalai's $3^d$ Conjecture

Published 16 Nov 2022 in math.CO and math.DG | (2211.09215v2)

Abstract: Suppose that $C$ is a centrally symmetric $d$-dimensional convex polytope; in 1989 Kalai conjectured that $C$ has at least $3^d$ facets. We prove this result if there are $d$ hyperplanes with orthogonal normal vectors so that $C$ is symmetric about all of them.

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