The Poisson's ratio defines a material’s geometrical response to stretch or compression. For natural isotropic materials, its value typically ranges from -1 to 0.5. Poisson's ratio metamaterials are architected structures aiming for specific values. This metamaterial class has three groups categorized by their values of Poisson's ratio. Metastructures that are auxetic [1] possess a negative Poisson’s ratio; anepirretic [2] have a zero Poisson’s ratio; and meiotic [2,3] have a positive Poisson’s ratio. Auxetic structures are the most common and exist both in a chiral and achiral form. Chiral objects exist in two enantiomorphs, the object and its mirror image. Joining these two enantiomorphs results in creating an achiral object.

Based on this aspect of we are proposing a minimal planar Poisson’s ratio chiral structure, that can be in both a meiotic (Figure 1.a) and in an auxetic shape (Figure 1.b). This three-beam structure exhibit large Poisson’s ratios (Figure 1.c shows a typical the range from -6 to 2.5). In addition, we are proposing a three-step design method for the design of 2D Poisson’s ratio metastructures. This method is composed of two topological transformations, the achiralisation process which transforms a chiral object in an achiral one, and, the copy-rotation process which creates and connects N copies of an object around a centre of rotation (Figure 1.d). The two transformations can be combined to design more complex structures from the composition of the two transformations to create complex Poisson’s ratio metamaterials. In addition, we investigate these metamaterials form the perspective of the surface strain, which links to the surface compressibility.

The design method can generate an infinite amount of structures both existing and novel ones. The structures are categorized in twelve groups displaying negative, zero and positives values of the Poisson’s ratio. We proposed a naming protocol to reference these structures while encoding the transformations applied to the base structure. Additionally, we propose to tessellate the metastructures following the Archimedean tiling method.