Non-lattice-periodic tilings of R3 by single polycubes

Authors:
I. Gambini;L. Vuillon
Affiliations:
Laboratoire dInformatique Fondamentale de Marseille, CNRS UMR 6166, Aix Marseille Univ, F-13288 Marseille Cedex 9, France;Laboratoire de mathématiques, CNRS UMR 5127, Université de Savoie, 73376 Le Bourget-du-lac Cedex, France
Venue:
Theoretical Computer Science
Year:
2012

Citing 2
Cited 0

On the tiling by translation problem

Discrete Applied Mathematics
An aperiodic hexagonal tile

Journal of Combinatorial Theory Series A

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Abstract

In this paper, we study a class of polycubes that tile the space by translation in a non-lattice-periodic way. More precisely, we construct a family of tiles indexed by integers with the property that T"k is a tile having k=2 as anisohedral number. That is k copies of T"k are assembled by translation in order to form a metatile. We prove that this metatile is a lattice-periodic tile while T"k is not a lattice-periodic tile.