The regulation of nuclear state by the cytoskeleton is an important part of cellular function. Actomyosin stress fibres, microtubules and intermediate filaments have distinct and complementary roles in integrating the nucleus into its environment and influencing its mechanical state. However, the interconnectedness of cytoskeletal networks makes it difficult to dissect their individual effects on the nucleus. We use simple image analysis approaches to characterize nuclear state, estimating nuclear volume, Poisson's ratio, apparent elastic modulus and chromatin condensation. By combining them with cytoskeletal quantification, we assess how cytoskeletal organization regulates nuclear state. We report for a number of cell types that nuclei display auxetic properties. Furthermore, stress fibres and intermediate filaments modulate the mechanical properties of the nucleus and also chromatin condensation. Conversely, nuclear volume and its gross morphology are regulated by intracellular outward pulling forces exerted by myosin. The modulation exerted by the cytoskeleton onto the nucleus results in changes that are of similar magnitude to those observed when the nucleus is altered intrinsically, inducing chromatin decondensation or cell differentiation. Our approach allows pinpointing the contribution of distinct cytoskeletal proteins to nuclear mechanical state in physio- and pathological conditions, furthering our understanding of a key aspect of cellular behaviour.