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Mathematical Notes

, Volume 92, Issue 3–4, pp 345–355 | Cite as

Belt distance between facets of space-filling zonotopes

  • A. I. GarberEmail author
Article

Abstract

To every d-dimensional polytope P with centrally symmetric facets one can assign a “subway map” such that every line of this “subway” contains exactly the facets parallel to one of the ridges of P. The belt diameter of P is the maximum number of subway lines one needs to use to get from one facet to another. We prove that the belt diameter of a d-dimensional space-filling zonotope does not exceed ⌈log2(4/5)d⌉.

Keywords

zonotope parallelohedron polytope belt diameter Voronoi’s conjecture tiling Dirichlet-Voronoi polytope canonical scaling of a tiling 

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Yaroslavl State UniversityYaroslavlRussia

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