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: the class of parallelepipeds, the class of centrally symmetric polytopes, and the class of Cayley sums $\text{Cay}(P,Q)$ 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.

11 pages, 7 figures

References in corpus (4)

• Existence of unimodular triangulations - positive results
• Problems on Minkowski sums of convex lattice polytopes
• Cayley sums and Minkowski sums of lattice polytopes
• Smooth centrally symmetric polytopes in dimension 3 are IDP