Auxetic metamaterials are engineered structures characterized by a unique property - a negative Poisson's ratio, enabling them to expand or contract perpendicularly to stretch or compression. Their exceptional attributes, such as energy absorption and fracture resistance, make them promising for diverse applications.

Nevertheless, the lack of an efficient design method has impeded their widespread development. To address this, we introduce a minimal 2D auxetic structure and a design approach involving two geometric transformations. This method not only replicates existing auxetic structures but also fosters the creation of novel ones, classifying them into six distinct categories.

To enhance understanding and standardization, we propose a naming protocol and define the associated unit cell. Additionally, we explore tessellations within this framework. Furthermore, we analyze auxetic structures from a surface strain perspective, closely related to Poisson's ratio, Bulk modulus, and compressibility.