Belt distance between facets of space-filling zonotopesстатья
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Аннотация: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 aOElog(2)(4/5)daOE parts per thousand.