Non-lattice-periodic tilings of R-3 by single polycubes

作者：Gambini I; Vuillon L^*

来源：Theoretical Computer Science, 2012, 432: 52-57.

DOI：10.1016/j.tcs.2012.01.014

• Tilings of R-3
• Polycubes
• Tilings by translation
• Lattice-periodic tilings
• Anisohedral number

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 %26gt;= 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.

• 出版日期2012-5-11