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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).

 Autoría: Codenotti G., Santos F.,

 Fuente: Proceedings of the American Mathematical Society, 2020, 148(2), 835-850

 Editorial: American Mathematical Society

 Fecha de publicación: 01/02/2020

 Nº de páginas: 16

 Tipo de publicación: Artículo de Revista

 DOI: 10.1090/proc/14721

 ISSN: 0002-9939,1088-6826

 Proyecto español: MTM2017-83750-P

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

Authorship

CODENOTTI, GIULIA