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Fig. 1. Experimental setup and data analysis. (a) Animal cap tissue was dissected from stage-10 Xenopus laevis embryos and cultured on PDMS membrane. (b) Side-view confocal image of the animal cap (top:apical; bottom:basal), stained for microtubules (red), beta-catenin (green) and DNA (blue). A mitotic spindle is visible in the centremost apical cell. The animal cap is a multi-layered epithelial tissue; we analyse just the outer, apical, cell layer. (c) The apical cell layer of the animal cap tissue is imaged live using confocal microscopy (green, GFP-\documentclass[12pt]{minimal}
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}{}$\alpha$\end{document}-tubulin; red, cherry-histone2B). (d) The cell edges are manually traced and cell shapes are derived computationally, being polygonized using the positions of cell junctions. (e) Mean normalized area as a function of polygonal class showing mean and one standard deviation, from experiments (solid and shaded) and simulation (dashed) with parameters \documentclass[12pt]{minimal}
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}{}$P_{\mathrm{ext}}=0$\end{document}. Cell areas were normalized relative to the mean of each experiment. (f) Circularity as a function of polygonal class showing mean and one standard deviation, from experiments (solid and shaded) and simulation (dashed) using the same parameters as in (e). (g) Proportions of total cells in each polygonal class in experiments (left bar) and simulations (right bar). Error bars represent \documentclass[12pt]{minimal}
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Fig. 2. Representation of disordered cell geometry. Cell \documentclass[12pt]{minimal}
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Fig. 3. Computational validation of the predicted alignment between principal axis of stress and shape, for \documentclass[12pt]{minimal}
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Fig. 4. (a) \documentclass[12pt]{minimal}
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Fig. 5. (a, c) Curves show \documentclass[12pt]{minimal}
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Fig. 6. (a) A map of the variance of \documentclass[12pt]{minimal}
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Fig. 7. Dependence of cell geometry on model parameters, using five unique simulations with 800 cells (4000 cells total) in a periodic box under zero net external pressure. (a) Mean circularity of cells per polygonal class, at parameter values indicated by corresponding symbols in \documentclass[12pt]{minimal}
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Fig. 8. Visualizing the effect of peripheral stress on network packing geometry. 800 cells were simulated in boxes of width \documentclass[12pt]{minimal}
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Fig. 9. Results of parameter fitting. (a) Heat map showing value of the likelihood function (4.1) across a uniform grid in valid parameter space. The simulated monolayers used were the same as those in Figs 6 and 7. For each monolayer, the mean areas per polygonal class were calculated and used to evaluate (4.1). The likelihood was maximized at \documentclass[12pt]{minimal}
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Fig. D1. (a) An example of force chains in a monolayer, with 800 cells and \documentclass[12pt]{minimal}
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