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Hollow polytopes of large width

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 (resp., 404) and of width 15 (resp., 408). We also construct a hollow (nonlattice) tetrahedron of width 2 + ?2, and we conjecture that this is the maximum width among 3-dimensional hollow convex bodies. We show that the maximum lattice width grows (at least) additively with d. In particular, the constructions above imply the existence of hollow lattice polytopes (resp., hollow simplices) of arbitrarily large dimension d and width  1.14d (resp.,  1.01d).

 Fuente: Proceedings of the American Mathematical Society Volume 148, Number 2, February 2020, Pages 835-850

Editorial: American Mathematical Society

 Fecha de publicación: 01/02/2020

Nº de páginas: 16

Tipo de publicación: Artículo de Revista

ISSN: 0002-9939,1088-6826

Proyecto español: MTM2017-83750-P

Url de la publicación: https://doi.org/10.1090/proc/14721