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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm9059https://doi.org/10.4213/mzm9059 https://www.mathnet.ru/eng/mzm/v92/i3/p381
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Abstract page: | 532 | Full-text PDF : | 179 | References: | 96 | First page: | 26 |
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