In principle, designing and synthesizing almost any class of colloidal crystal is possible. Nonetheless, the deliberate and rational formation of colloidal quasicrystals has been difficult to achieve. Here we describe the assembly of colloidal quasicrystals by exploiting the geometry of nanoscale decahedra and the programmable bonding characteristics of DNA immobilized on their facets. This process is enthalpy-driven, works over a range of particle sizes and DNA lengths, and is made possible by the energetic preference of the system to maximize DNA duplex formation and favour facet alignment, generating local five- and six-coordinated motifs. This class of axial structures is defined by a square–triangle tiling with rhombus defects and successive on-average quasiperiodic layers exhibiting stacking disorder which provides the entropy necessary for thermodynamic stability. Taken together, these results establish an engineering milestone in the deliberate design of programmable matter.

原则上，设计和合成几乎任何类别的胶体晶体都是可能的。尽管如此，胶体准晶的有意且合理的形成一直难以实现。在这里，我们通过利用纳米级十面体的几何形状和固定在其面上的 DNA 的可编程键合特性来描述胶体准晶体的组装。该过程是由焓驱动的，适用于一系列颗粒尺寸和 DNA 长度，并且通过系统的能量偏好来实现，以最大限度地形成 DNA 双链体并有利于面对齐，从而生成局部五配位和六配位基序。这类轴向结构由具有菱形缺陷的方三角形平铺和表现出堆叠无序的连续平均准周期层定义，这提供了热力学稳定性所需的熵。总而言之，这些结果在可编程物质的精心设计中树立了一个工程里程碑。