Molecular tessellations are known in solid state systems and their formation is often induced or supported by a periodic surface lattice. Here we discover a complex tessellation on the 10 nm length scale, spontaneously formed in the highly dynamic liquid crystalline state. It is composed of overlapping dodecagonal supertiles combining prismatic cells with triangular and square cross sections. This complex honeycomb occurs between a triangular honeycomb at high and a square at low temperature, being opposite to the sequence expected for a thermal expansion of the side chains in the prismatic cells. Formation of the supertiles is supported by the segregation of alkyl chains with different length. The emergent behaviour of this complex soft matter structure is demonstrated, and intriguing connections between self-assembly on surfaces, in liquid crystals, and in block copolymers are drawn. Moreover, the tessellation represents a close approximant of the elusive columnar liquid quasicrystal with dodecagonal symmetry.

分子镶嵌在固态系统中是已知的，它们的形成通常由周期性表面晶格诱导或支持。在这里，我们发现了 10 nm 长度尺度上的复杂镶嵌，它在高度动态的液晶状态下自发形成。它由重叠的十二边形超分片组成，这些超分片结合了具有三角形和正方形横截面的棱柱形电池。这种复杂的蜂窝出现在高温下的三角形蜂窝和低温下的正方形蜂窝之间，与棱柱形电池中侧链热膨胀的预期顺序相反。supertiles 的形成是由不同长度的烷基链的分离支持的。展示了这种复杂软物质结构的涌现行为，以及表面自组装之间有趣的联系，在液晶和嵌段共聚物中绘制。此外，镶嵌代表了具有十二边形对称性的难以捉摸的柱状液体准晶体的近似值。