Quasicrystals are intriguing structures that have long-range positional correlations but no periodicity in real space, and typically with rotational symmetries that are ‘forbidden’ in conventional periodic crystals. Here, we present a two-dimensional columnar liquid quasicrystal with dodecagonal symmetry. Unlike previous dodecagonal quasicrystals based on random tiling, a honeycomb structure based on a strictly quasiperiodic tessellation of tiles is observed. The structure consists of dodecagonal clusters made up of triangular, square and trapezoidal cells that are optimal for local packing. To maximize the presence of such dodecagonal clusters, the system abandons periodicity but adopts a quasiperiodic structure that follows strict packing rules. The stability of random-tiling dodecagonal quasicrystals is often attributed to the entropy of disordering when strict tiling rules are broken, at the sacrifice of the long-range positional order. However, our results demonstrate that quasicrystal stability may rest on energy minimization alone, or with only minimal entropic intervention.

准晶体是一种有趣的结构，具有长程位置相关性，但在真实空间中没有周期性，并且通常具有旋转对称性，这在传统周期性晶体中是“禁止的”。在这里，我们提出了一种具有十二边形对称性的二维柱状液体准晶。与之前基于随机拼接的十二边形准晶体不同，观察到基于严格准周期拼接拼接的蜂窝结构。该结构由三角形、方形和梯形细胞组成的十二边形簇组成，最适合局部堆积。为了最大化这种十二边形簇的存在，系统放弃了周期性，而是采用了遵循严格包装规则的准周期结构。随机拼接十二边形准晶体的稳定性通常归因于严格的拼接规则被打破时的无序熵，牺牲了长程位置顺序。然而，我们的结果表明，准晶稳定性可能仅依赖于能量最小化，或者仅依赖于最小的熵干预。