Intracellular and extracellular mechanical forces play a crucial role during tissue growth, modulating nuclear shape and function and resulting in complex collective cell behaviour. However, the mechanistic understanding of how the orientation, shape, symmetry and homogeneity of cells are affected by environmental geometry is still lacking. Here we investigate cooperative cell behaviour and patterns under geometric constraints created by topographically patterned substrates. We show how cells cooperatively adopt their geometry, shape, positioning of the nucleus and subsequent proliferation activity. Our findings indicate that geometric constraints induce significant squeezing of cells and nuclei, cytoskeleton reorganization, drastic condensation of chromatin resulting in a change in the cell proliferation rate and the anisotropic growth of cultures. Altogether, this work not only demonstrates complex non-trivial collective cellular responses to geometrical constraints but also provides a tentative explanation of the observed cell culture patterns grown on different topographically patterned substrates. These findings provide important fundamental knowledge, which could serve as a basis for better controlled tissue growth and cell-engineering applications.