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Belt distance between facets of space-filling zonotopes

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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⌉.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. I. Garber

  2. Yaroslavl State University, Yaroslavl, Russia

    A. I. Garber

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  1. A. I. Garber
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Correspondence to A. I. Garber.

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Original Russian Text © A. I. Garber, 2012, published in Matematicheskie Zametki, 2012, Vol. 92, No. 3, pp. 381–394.

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Garber, A.I. Belt distance between facets of space-filling zonotopes. Math Notes 92, 345–355 (2012). https://doi.org/10.1134/S0001434612090064

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  • DOI: https://doi.org/10.1134/S0001434612090064

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