A two-vertex theorem for normal tilings
| Autor: | Gábor Domokos, Ákos G. Horváth, Krisztina Regős |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Popis: | We regard a smooth, $d=2$-dimensional manifold $\mathcal{M}$ and its normal tiling $M$, the cells of which may have non-smooth or smooth vertices (at the latter, two edges meet at 180 degrees.) We denote the average number (per cell) of non-smooth vertices by $\bar v^{\star}$ and we prove that if $M$ is periodic then $v^{\star} \geq 2$ and we show the same result for the monohedral case by an entirely different argument. Our theory also makes a closely related prediction for non-periodic tilings. In 3 dimensions we show a monohedral construction with $\bar v^{\star}=0$. Comment: 11 pages, 4 figures |
| Databáze: | OpenAIRE |
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