
Journal for Geometry and Graphics 27 (2023), No. 2, 159169 Copyright Heldermann Verlag 2023 On Spiral Structures in Tilings Jessa Camille Duero Inst. of Math. Sciences and Physics, University of the Philippines, Los Bańos, Philippines jcduero@up.edu.ph Bernhard Klaassen Fraunhofer Research Institution, Bochum, Germany bernhard.klaassen@scai.fraunhofer.de We investigate the existence of spiral structure in certain types of tilings. Following a question posed by Branko Grünbaum, it is demonstrated that all Archimedean tilings can be partitioned in a spiral like manner thereby fulfilling a definition given in 2017 for this visual effect. Furthermore, to show that this is not possible for every arbitrary periodic tiling, non "spirable" examples are constructed in the sense of this definition. Lastly, an intuitive result for onearmed spirals is established: onearmed spirals and periodic tilings cannot coexist. Keywords: Tiling, spiral tiling, periodic, onearmed spiral. MSC: 52C20. [ Fulltextpdf (2814 KB)] 