Rotationally Symmetric Tilings with Convex Pentagons and Hexagons
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2015
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| _version_ | 1866908428958433280 |
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| author | Klaassen, Bernhard |
| author_facet | Klaassen, Bernhard |
| contents | In contrast to many known results concerning periodic tilings of the Euclidean plane with pentagons, here tilings with rotational symmetry are investigated. A certain class of convex pentagons is introduced. It can be shown that for any given symmetry type $\mathbf{C}_{n}$ or $\mathbf{D}_{n}$ there exists a monohedral tiling generated by a pentagon from this class. For $n>1$ each of these tilings is also a spiral tiling with $n$ arms. As a byproduct it follows that the same holds for convex hexagons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1509_06297 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Rotationally Symmetric Tilings with Convex Pentagons and Hexagons Klaassen, Bernhard Metric Geometry Combinatorics 52C20 In contrast to many known results concerning periodic tilings of the Euclidean plane with pentagons, here tilings with rotational symmetry are investigated. A certain class of convex pentagons is introduced. It can be shown that for any given symmetry type $\mathbf{C}_{n}$ or $\mathbf{D}_{n}$ there exists a monohedral tiling generated by a pentagon from this class. For $n>1$ each of these tilings is also a spiral tiling with $n$ arms. As a byproduct it follows that the same holds for convex hexagons. |
| title | Rotationally Symmetric Tilings with Convex Pentagons and Hexagons |
| topic | Metric Geometry Combinatorics 52C20 |
| url | https://arxiv.org/abs/1509.06297 |