Geodesic
On Spiral Structures in Tilings
Journal for geometry and graphics, Tome 27 (2023) no. 2, pp. 159-169 Cet article a éte moissonné depuis la source Heldermann Verlag

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We investigate the existence of spiral structure in certain types of tilings. Following a question posed by Branko Gr�nbaum, 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.
Classification : 52C20
Mots-clés : Tiling, spiral tiling, periodic, one-armed spiral 
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     author = {J. C. Duero and B. Klaassen },
     title = {On {Spiral} {Structures} in {Tilings}},
     journal = {Journal for geometry and graphics},
     pages = {159--169},
     year = {2023},
     volume = {27},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2023_27_2_JGG_2023_27_2_a3/}
}
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J. C. Duero; B. Klaassen . On Spiral Structures in Tilings. Journal for geometry and graphics, Tome 27 (2023) no. 2, pp. 159-169. http://geodesic.mathdoc.fr/item/JGG_2023_27_2_JGG_2023_27_2_a3/