How many faces can polycubes of lattice tilings by translation of R3 have? - Université Grenoble Alpes Accéder directement au contenu
Article Dans Une Revue The Electronic Journal of Combinatorics Année : 2011

How many faces can polycubes of lattice tilings by translation of R3 have?

Résumé

We construct a class of polycubes that tile the space by translation in a lattice- periodic way and show that for this class the number of surrounding tiles cannot be bounded. The first construction is based on polycubes with an L-shape but with many distinct tilings of the space. Nevertheless, we are able to construct a class of more complicated polycubes such that each polycube tiles the space in a unique way and such that the number of faces is 4k + 8 where 2k + 1 is the volume of the polycube. This shows that the number of tiles that surround the surface of a space-filler cannot be bounded.
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Dates et versions

hal-00943569 , version 1 (07-02-2014)

Identifiants

  • HAL Id : hal-00943569 , version 1

Citer

Ian Gambini, Laurent Vuillon. How many faces can polycubes of lattice tilings by translation of R3 have?. The Electronic Journal of Combinatorics, 2011, 18, pp.#P199. ⟨hal-00943569⟩
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