The most striking feature of conventional quasicrystals is their non-traditional symmetry characterized by icosahedral, dodecagonal, decagonal or octagonal axes^1,2,3,4,5,6. The symmetry and the aperiodicity of these materials stem from an irrational ratio of two or more length scales controlling their structure, the best-known examples being the Penrose^7,8 and the Ammann–Beenker^9,10 tiling as two-dimensional models related to the golden and the silver mean, respectively. Surprisingly, no other metallic-mean tilings have been discovered so far. Here we propose a self-similar bronze-mean hexagonal pattern, which may be viewed as a projection of a higher-dimensional periodic lattice with a Koch-like snowflake projection window. We use numerical simulations to demonstrate that a disordered variant¹¹ of this quasicrystal can be materialized in soft polymeric colloidal particles with a core–shell architecture^{12,13,14,15,16,17}. Moreover, by varying the geometry of the pattern we generate a continuous sequence of structures, which provide an alternative interpretation of quasicrystalline approximants observed in several metal–silicon alloys¹⁸.

常规准晶体最显着的特征是它们的非传统对称性，其特征为二十面体，十二边形，十边形或八边形轴^1,2,3,4,5,6。这些材料的对称性和非周期性是由两个或更多个长度尺度的无理比率控制的，这些长度尺度控制它们的结构，最著名的例子是Penrose ^7,8和Ammann–Beenker ^9,10平铺为分别与黄金和白银均值有关的二维模型。令人惊讶的是，到目前为止，还没有发现其他金属均值平铺。在这里，我们提出了一种自相似的古铜色均方六边形图案，可以将其视为带有科赫式雪花投影窗口的高维周期晶格的投影。我们使用数值模拟来证明，这种准晶体的无序变体¹¹可以在具有核-壳结构的软聚合物胶体颗粒中实现^{12、13、14、15、16、17}。此外，通过改变图案的几何形状，我们生成了连续的结构序列，这为在几种金属-硅合金中观察到的准晶体近似物提供了另一种解释¹⁸。