Substitution discrete plane tilings with $2n$-fold rotational symmetry for odd n
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866910617590300672 |
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| author | Kari, Jarkko Lutfalla, Victor H. |
| author_facet | Kari, Jarkko Lutfalla, Victor H. |
| contents | We study substitution tilings that are also discrete plane tilings, that is, satisfy a relaxed version of cut-and-projection. We prove that the Sub Rosa substitution tilings with a 2n-fold rotational symmetry for odd n greater than 5 defined by Kari and Rissanen are not discrete planes, and therefore not cut-and-project tilings either. We then define new Planar Rosa substitution tilings with a 2n-fold rotational symmetry for any odd n, and show that these satisfy the discrete plane condition. The tilings we consider are edge-to-edge rhombus tilings. We give an explicit construction for the 10-fold case, and provide a construction method for the general case of any odd n. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_01879 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Substitution discrete plane tilings with $2n$-fold rotational symmetry for odd n Kari, Jarkko Lutfalla, Victor H. Discrete Mathematics Combinatorics We study substitution tilings that are also discrete plane tilings, that is, satisfy a relaxed version of cut-and-projection. We prove that the Sub Rosa substitution tilings with a 2n-fold rotational symmetry for odd n greater than 5 defined by Kari and Rissanen are not discrete planes, and therefore not cut-and-project tilings either. We then define new Planar Rosa substitution tilings with a 2n-fold rotational symmetry for any odd n, and show that these satisfy the discrete plane condition. The tilings we consider are edge-to-edge rhombus tilings. We give an explicit construction for the 10-fold case, and provide a construction method for the general case of any odd n. |
| title | Substitution discrete plane tilings with $2n$-fold rotational symmetry for odd n |
| topic | Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2010.01879 |