Abstract
We construct the first known hollow lattice polytopes of width larger than dimension: a hollow lattice polytope (resp., a hollow lattice simplex) of dimension 14 14 (resp., 404 404 ) and of width 15 15 (resp., 408 408 ). We also construct a hollow (nonlattice) tetrahedron of width 2 + 2 2+\sqrt 2 , and we conjecture that this is the maximum width among 3 3 -dimensional hollow convex bodies. We show that the maximum lattice width grows (at least) additively with d d . In particular, the constructions above imply the existence of hollow lattice polytopes (resp., hollow simplices) of arbitrarily large dimension d d and width ≃ 1.14 d \simeq 1.14 d (resp., ≃ 1.01 d \simeq 1.01 d ).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
