<p>For a long time, people have always hoped to achieve aperiodic tiling of a plane using a single monotile. This vision became a reality with mathematicians’ discovery of the “Einstein” monotile (also known as the “hat” monotile). Such aperiodic tiled structures typically exhibit topological anisotropy, making their mechanical properties significantly superior to those of periodic structures. This study focuses on the application of aperiodically tiled “hat” monotiles in honeycomb metamaterial structures. From the perspective of information entropy, it reveals that the enhancement in mechanical performance of these structures stems from the higher entropy values associated with their aperiodic configurations. To quantify the disorder of aperiodic structures, this research proposes a topological entropy quantification expression applicable to disordered configurations. To validate the mechanical performance of high-entropy structures, specimens were fabricated via 3D printing and mechanical experiments were conducted; meanwhile, finite element analysis was performed using ABAQUS software for comparative analysis. Results show that, under the same conditions, high-entropy structures formed by the aperiodic stacking of unit cells exhibit a significant improvement in mechanical performance compared to low-entropy structures formed by periodic stacking. The conclusions drawn from this study are generalizable and may provide useful references for future material and structural design.</p>