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Mat. Zametki, 2012, Volume 92, Issue 3, Pages 381–394 (Mi mz9059)  

This article is cited in 1 scientific paper (total in 1 paper)

Belt Distance Between Facets of Space-Filling Zonotopes

A. I. Garberab

a M. V. Lomonosov Moscow State University
b P. G. Demidov Yaroslavl State University

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 $\lceil\log_2(4/5)d\rceil$.

Keywords: zonotope, parallelohedron, polytope, belt diameter, Voronoi's conjecture, tiling, Dirichlet–Voronoi polytope, canonical scaling of a tiling

DOI: https://doi.org/10.4213/mzm9059

Full text: PDF file (561 kB)
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English version:
Mathematical Notes, 2012, 92:3, 345–355

Bibliographic databases:

Document Type: Article
UDC: 514
Received: 16.12.2010
Revised: 12.02.2011

Citation: A. I. Garber, “Belt Distance Between Facets of Space-Filling Zonotopes”, Mat. Zametki, 92:3 (2012), 381–394; Math. Notes, 92:3 (2012), 345–355

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  • https://doi.org/10.4213/mzm9059
  • http://mi.mathnet.ru/eng/mz/v92/i3/p381

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Garber A., “Belt Diameter of Pi-Zonotopes”, Eur. J. Comb., 34:5 (2013), 923–933  crossref  mathscinet  zmath  isi  elib  scopus
  • Математические заметки Mathematical Notes
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