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Matematicheskie Zametki, 2012, Volume 92, Issue 3, Pages 381–394
DOI: https://doi.org/10.4213/mzm9059 (Mi mzm9059) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
Full-text PDF (561 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm9059
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.
Received: 16.12.2010
Revised: 12.02.2011
English version:
Mathematical Notes, 2012, Volume 92, Issue 3, Pages 345–355
DOI: https://doi.org/10.1134/S0001434612090064
Bibliographic databases:
Document Type: Article
UDC: 514
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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