arXiv Open Access 2022

A three tile 6-fold golden-mean tiling

Sam Coates Toranosuke Matsubara Akihisa Koga

Lihat Sumber

Abstrak

We present a multi-edge-length aperiodic tiling which exhibits 6--fold rotational symmetry. The edge lengths of the tiling are proportional to 1:$τ$, where $τ$ is the golden mean $\frac{1+\sqrt{5}}{2}$. We show how the tiling can be generated using simple substitution rules for its three constituent tiles, which we then use to demonstrate the bipartite nature of the tiling vertices. As such, we show that there is a relatively large sublattice imbalance of $1/[2τ^2]$. Similarly, we define allowed vertex configurations before analysing the tiling structure in 4-dimensional hyperspace.

Topik & Kata Kunci

cond-mat.other cond-mat.soft

Penulis (3)

Sam Coates

Toranosuke Matsubara

Akihisa Koga

Format Sitasi

APA MLA BibTeX

Coates, S., Matsubara, T., Koga, A. (2022). A three tile 6-fold golden-mean tiling. https://arxiv.org/abs/2211.00127

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Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓