Non-lattice-periodic tilings of \(\mathbb R^3\) by single polycubes

DOI10.1016/j.tcs.2012.01.014zbMath1243.05061OpenAlexW2063248089MaRDI QIDQ428854

Laurent Vuillon, Ian Gambini

Publication date: 25 June 2012

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.tcs.2012.01.014

zbMATH Keywords

polycubesanisohedral numberlattice-periodic tilingstilings by translationtilings of \(\mathbb R^{3}\)

Mathematics Subject Classification ID

Three-dimensional polytopes (52B10) Combinatorial aspects of tessellation and tiling problems (05B45) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Cites Work

• How many faces can the polycubes of lattice tilings by translation of \(\mathbb R^3\) have?
• An aperiodic hexagonal tile
• Polygons, polyominoes and polycubes
• On the tiling by translation problem
• The hexagonal parquet tiling: \(k\)-isohedral monotiles with arbitrarily large \(k\).
• On translating one polyomino to tile the plane
• Isohedral polyomino tiling of the plane
• Forcing nonperiodicity with a single tile
• Arbitrary versus periodic storage schemes and tessellations of the plane using one type of polyomino
• Tilings with congruent tiles
• An algorithm for deciding if a polyomino tiles the plane
• Checker Boards and Polyominoes

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