Recent research into lithium ion battery storage particles has seen the development of many models to predict lithiation stresses generated during operation, and their effects on performance. Due to computational considerations most of the particles studied have idealized geometry with smooth surfaces, such as spheres. In reality, storage particles used in battery electrodes are acicular and have sharp edges and corners. In order to study the effect of these edges and corners on the generation of lithiation stress, we perform a parameter study on the development of lithiation strain and the resulting stress in cubic-shaped particles. We use a previously developed coupled stress-diffusion model, as well as three non-dimensional parameters, to quantify the stress response of cubic-shaped particles as a function of their material properties. Our results show that a change in material properties can lead to differences in both the value of maximum stress as well as its location in the particle. Both lithium insertion into and extraction from the particle are considered.