From solar supergranulation to salt flat in Bolivia, from veins on leaves to cells on Drosophila wing discs, polygon-based networks exhibit great complexities, yet similarities and consistent patterns emerge. Based on analysis of 99 polygonal tessellations of a wide variety of physical origins, this work demonstrates the ubiquity of an exponential distribution in the squared norm of the deformation tensor, E 2 , which directly leads to the ubiquitous presence of Gamma distributions in polygon aspect ratio as recently demonstrated by Atia et al. [Nat. Phys. 14 , 613 (2018)]. In turn an analytical approach is developed to illustrate its origin. E 2 relates to most energy forms, and its Boltzmann-like feature allows the definition of a pseudo-temperature that promises utility in a thermodynamic ensemble framework.