Converting non-periodic tilings with Tile(1, 1) into tilings with three types of pentagons, II

Sugimoto, Teruhisa

doi:10.51094/jxiv.1282

##article.authors##

Sugimoto, Teruhisa The Interdisciplinary Institute of Science, Technology and Art https://orcid.org/0000-0003-0961-3236

DOI:

https://doi.org/10.51094/jxiv.1282

キーワード:

pentagon、 rhombus、 tiling、 non-periodic、 aperiodic

抄録

In the previous study [6], we demonstrated that non-periodic tilings generated using Tile(1, 1) can be converted into non-periodic tilings with three types of pentagons. However, these results excluded the case where the conversion is performed after subdividing the original rhombus into smaller similar rhombuses. In this manuscript, we examine the case in which the conversion is performed after subdividing the original rhombus into smaller similar rhombuses. We describe the similarities and differences between the pentagonal tilings obtained by conversion with and without subdivision of the original rhombus into smaller similar rhombuses.

利益相反に関する開示

The authors declare no conflicts of interest associated with this manuscript.

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引用文献

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Sugimoto, T., (2022). Converting tilings with multiple types of rhombuses to pentagonal tilings, arXiv:2203.04457 (accessed on 16 May 2025).

Sugimoto, T., (2023). Converting non-periodic tiling with Tile(1,1) to tilings with three types of pentagons, I, arXiv:2307.08184 (accessed on 16 May 2025).

Sugimoto, T., Supplement of the paper "Converting non-periodic tiling with Tile(1, 1) into tilings with three types of pentagons," https://tilingpackingcovering.web.fc2.com/Ts_with_3-types_pentagons-e.html (accessed on 16 May 2025).

Sugimoto, T., Supplement of the paper "Converting non-periodic tiling with Tile(1, 1) into tilings with three types of pentagons," https://tilingpackingcovering.web.fc2.com/Th_with_3-types_pentagons-e.html (accessed on 16 May 2025).