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Title: Exploring symmetry in rosettes of Truchet tiles
Author: Hall, Andreia
Almeida, Paulo J.
Teixeira, Ricardo
Keywords: Truchet tiles
Rosette symmetry groups
Recreational mathematics
Issue Date: 2019
Publisher: Taylor & Francis
Abstract: In 1704 the French priest S ebastien Truchet published a paper where he explored and counted patterns made up from a square divided by a diagonal line into two colored parts,, now known as a Truchet tile. A few years later, Father Dominique Douat continued Truchet's work and published a book in 1722 containing many more patterns and further counts of con gurations. In this paper, we extend the work introduced by Truchet and Douat by considering all possible rosettes made up of an mXn array of square or non-square Truchet tiles. We then classify the rosettes according to their symmetry group and count all the distinct rosettes in each group, for all possible sizes. The results are summarized in a separate section where we further analyze the asymptotic behavior of the counts for square arrays. Finally, some applications are shown using two types of square flexagons.
Peer review: yes
DOI: 10.1080/17513472.2019.1581963
ISSN: 1751-3472
Appears in Collections:CIDMA - Artigos
DMat - Artigos
PSG - Artigos

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