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• W69425352 abstract "We study multiple tilings of 3-dimensional Euclidean space by a convex body. In a multiple tiling, a convex body P is translated with a discrete multiset Λ in such a way that each point of ℝ d gets covered exactly k times, except perhaps the translated copies of the boundary of P. It is known that all possible multiple tilers in ℝ3 are zonotopes. In ℝ2 it was known by the work of M. Kolountzakis [9] that, unless P is a parallelogram, the multiset of translation vectors Λ must be a finite union of translated lattices (also known as quasi periodic sets). In that work [9] the author asked whether the same quasi-periodic structure on the translation vectors would be true in ℝ3. Here we prove that this conclusion is indeed true for ℝ3." @default.
• W69425352 created "2016-06-24" @default.
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• W69425352 date "2013-01-01" @default.
• W69425352 modified "2023-09-26" @default.
• W69425352 title "Extended abstract for structure results for multiple tilings in 3D" @default.
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• W69425352 doi "https://doi.org/10.1007/978-88-7642-475-5_30" @default.
• W69425352 hasPublicationYear "2013" @default.
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