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Counting constraints in tissue mechanics

Understanding the mechanics of tissues is crucial to understanding multicellular life: All existing animals undergo gastrulation, where the embryo turns inside-out in the first step of the formation of the germ layers that will later become different parts of the body, like the brain, the skin or inner organs [1]. Two-dimensional, one cell thick epithelial cell sheets are at the heart of this transformation, and understanding the mechanics of these cobble-stone pavement like structures is necessary to understand embryo development and cell mechanics in general. In recent years, physics has started to contribute models of epithelial tissues. The most celebrated (but not the only) of these models is the Vertex model [2, 3], which in its most compact form corresponds to an energy functional