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The organization of cells within tissues plays a vital role in various biological processes, including development and morphogenesis. As a result, understanding how cells self-organize in tissues has been an active area of research. In our study, we explore a mechanistic model of cellular organization that represents cells as force dipoles that interact with each other via the tissue, which we model as an elastic medium. By conducting numerical simulations using this model, we are able to observe organizational features that are consistent with those obtained from vertex model simulations. This approach provides valuable insights into the underlying mechanisms that govern cellular organization within tissues, which can help us better understand the processes involved in development and disease.