An approach to study the effect of geometric parameters on the Poisson’s ratio of a three-dimensional re-entrant Cobalt Chrome Auxetic structure has been presented. The Auxetic mechanical structure has been realized with the help of Additive Manufacturing. The mechanical properties and Poisson’s ratio of the physical samples were determined using compression testing and Digital Image Correlation (DIC). A Finite Element model is used to estimate the Poisson’s ratio numerically. A Design of Experiments (DOE) and Finite Element Analysis (FEA) based optimization study is further performed in order to investigate the effects of the different geometric parameters on the Poisson’s ratio of the Auxetic samples. The DOE model is used to determine the values of the parameters for an optimal performance of the samples in terms of the observed Auxetic behaviour.