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Unimodular covers of \(3\)-dimensional parallelepipeds and Cayley sums
Abstract
We show that the following classes of lattice polytopes have unimodular covers, in dimension three: parallelepipeds, smooth centrally symmetric polytopes, and Cayley sums \(\operatorname{Cay}(P,Q)\) where the normal fan of \(Q\) refines that of \(P\). This improves results of Beck et al. (2018) and Haase et al. (2008) where the last two classes were shown to be IDP.
Mathematics Subject Classifications: 52B10, 52B20, 52C17
Keywords: Lattice polytopes, unimodular covers, integer decomposition property