Meiotic metamaterials are intricately designed structures characterized by a positive Poisson's ratio, surpassing the conventional limit of 0.5 observed in natural materials. This exceptional attribute allows them to contract or expand perpendicularly to the applied stretch or compression, respectively. Structures featuring a high positive Poisson's ratio exhibit a counter-intuitive negative compressibility behavior, holding significant promise for diverse applications spanning various domains. Despite the potential of Poisson's ratio metamaterials, including auxetic, anepirretic, and meiotic structures, their recent development has been hindered by the lack of efficient design methods. This paper aims to address this limitation, concentrating on the meiotic variant of a minimal 2D auxetic structure recently proposed. We employ a design method incorporating two topological transformations, not only enabling the creation of known meiotic structures but also facilitating the generation of new ones while understanding the impact of chirality. Additionally, the proposed method enables the categorization of these structures into three achiral families that present meiotic behavior and can exhibit negative linear compressibility and three chiral families that possess an auxetic behavior. Only the base chiral structure was found to exhibit a meiotic behavior while being chiral. In an effort to enhance comprehension and standardization, we introduce a naming protocol and define the associated unit cell for these structures. We also delve into the potential of tessellations within this framework. Finally, our study examines meiotic structures from the perspective of surface strain, a more general metrics, linked to the compressibility, providing further insights into their unique mechanical properties.

Auxetic metamaterials are architected structures that possess a unique property known as a negative Poisson's ratio. This remarkable characteristic enables them to expand or contract in a direction perpendicular to stretch or compression. Due to their exceptional attributes such as energy absorption and fracture resistance, these auxetic metamaterials hold great promise for various applications across multiple domains. However, the widespread development of these materials has been hindered by the absence of an efficient design method. Addressing this limitation, our work introduces a minimal 2D auxetic structure and a corresponding design approach that comprises two geometric transformations. This design method not only allows for the replication of existing auxetic structures but also facilitates the creation of novel structures. Additionally, it enables the classification of these structures into six distinct categories. To enhance the understanding and standardization of these structures, we propose a naming protocol and define their associated unit cell. Furthermore, we explore the possibilities of tessellations within this framework. Finally, we examine the auxetic structures from the perspective of surface strain, which is closely linked to the Poisson's ratio, the Bulk modulus and compressibility.