<p>To preserve the negative Poisson’s ratio characteristic of the re-entrant auxetic hexagonal structure while enhancing its mechanical properties, triangular folded ribs were incorporated into the re-entrant auxetic hexagonal structure (RAH), thereby establishing a novel triangular rib-enhanced re-entrant auxetic hexagonal structure (TRH). TRH specimens were prepared via additive manufacturing (AM) and subjected to quasi-static compression testing using a universal testing machine to investigate their mechanical properties. The results indicate that compared to RAH, the structure exhibited a second plateau in stress and demonstrated superior mechanical properties. For example, SEA increased by 75.5%. The influences of geometric parameters, such as rib thickness, apex radius, and apex angle size, on the mechanical properties and deformation behavior of the structure were investigated using experiments and numerical simulation. The variation in Poisson’s ratio of structural components and the failure mechanisms of this process was analyzed. The results indicate that by introduction of triangular ribs, TRH exhibits enhanced rigidity, strength, and energy-absorbing properties. Moreover, adjusting geometric parameters, such as rib thickness, can significantly alter the mechanical properties and deformation behavior of the structure, endows the re-entrant auxetic hexagonal structure with greater programmability, provides valuable insights for designing negative Poisson’s ratio honeycomb materials.</p>