Rectangle--triangle soft-matter quasicrystals with hexagonal symmetry
Abstract
Aperiodic (quasicrystalline) tilings, such as Penrose's tiling, can be built up from e.g. kites and darts, squares and equilateral triangles, rhombi or shield shaped tiles and can have a variety of different symmetries. However, almost all quasicrystals occurring in soft-matter are of the dodecagonal type. Here, we investigate a class of aperiodic tilings with hexagonal symmetry that are based on rectangles and two types of equilateral triangles. We show how to design soft-matter systems of particles interacting via pair potentials containing two length-scales that form aperiodic stable states with two different examples of rectangle--triangle tilings. One of these is the bronze-mean tiling, while the other is a generalization. Our work points to how more general (beyond dodecagonal) quasicrystals can be designed in soft-matter.
Cite
@article{arxiv.2208.02139,
title = {Rectangle--triangle soft-matter quasicrystals with hexagonal symmetry},
author = {Andrew J. Archer and Tomonari Dotera and Alastair M. Rucklidge},
journal= {arXiv preprint arXiv:2208.02139},
year = {2022}
}
Comments
15 pages, 13 figures. Submitted to Physical Review E. The data associated with this paper are openly available from the University of Leeds Data Repository at https://doi.org/10.5518/1188