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

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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

Grünbaum, B., and Shephard, G.C. (1987). Tilings and Patterns. W. H. Freeman and Company, New York, p p.15–56 (Chapter 1), pp.471–518 (Chapter 9), pp.519–582 (Chapter 10).

Smith, D., Myers, J. S., Kaplan, C. S., and Goodman-Strauss, C. (2024). An aperiodic monotile, Combinatorial Theory, 4 (1), 1–91. doi:10.5070/C64163843

Smith, D., Myers, J. S., Kaplan, C. S., and Goodman-Strauss, C. 2024). A chiral aperiodic monotile. Combinatorial Theory, 4 (2), 1–25. doi:10.5070/C64264241

Sugimoto, T., (2020). Pentagons and rhombuses that can form rotationally symmetric tilings, arXiv:2005.12709 (accessed on 16 May 2025).

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).

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投稿日時: 2025-06-03 00:16:40 UTC

公開日時: 2025-06-05 10:14:03 UTC
研究分野
数学