Morphogenesis is driven by small cell shape changes that modulate tissue organization. Apical surfaces of proliferating epithelial sheets have been particularly well studied. Currently, it is accepted that a stereotyped distribution of cellular polygons is conserved in proliferating tissues among metazoans. In this work, we challenge these previous findings showing that diverse natural packed tissues have very different polygon distributions. We use Voronoi tessellations as a mathematical framework that predicts this diversity. We demonstrate that Voronoi tessellations and the very different tissues analysed share an overriding restriction: the frequency of polygon types correlates with the distribution of cell areas. By altering the balance of tensions and pressures within the packed tissues using disease, genetic or computer model perturbations, we show that as long as packed cells present a balance of forces within tissue, they will be under a physical constraint that limits its organization. Our discoveries establish a new framework to understand tissue architecture in development and disease. Synopsis Cell shapes in naturally packed tissues have different polygon distributions. Voronoi tessellations-based analysis suggests that polygon frequencies are restricted by the distribution of cell areas, and that this restriction emanates from the balance of forces within the tissue. Cell shapes in natural packed tissues present very different polygon distributions. These patterns can be reproduced by Voronoi tessellations. Natural tissues and Voronoi diagrams share some geometrical properties. There is a physical constraint that limits the organization of natural tissues. Unbalance of forces within the natural tissue breaks this restriction. Cell shapes in naturally packed tissues have different polygon distributions. Voronoi tessellations-based analysis suggests that polygon frequencies are restricted by the distribution of cell areas, and that this restriction emanates from the balance of forces within the tissue. ; L.M.E. and D.S.‐G. are supported by the Ramón y Cajal Programme (PI13/01347), the Spanish Government grant BFU2011‐25734 and the ISCIII and FEDER funds PI13/01347. MT was funded by Sir Henry Wellcome Postdoctoral Fellowship (Grant No: 103095). YM was funded by a Medical Research Council Career Development Award Fellowship (Grant No: MR/L009056/1). ; Peer Reviewed