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Journal for Geometry and Graphics 27 (2023), No. 2, 159--169
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

Bernhard Klaassen
Fraunhofer Research Institution, Bochum, Germany

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 one-armed spirals is established: one-armed spirals and periodic tilings cannot coexist.

Keywords: Tiling, spiral tiling, periodic, one-armed spiral.

MSC: 52C20.

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