The remarkable property combinations of biological materials arise through the multi-scale arrangement of different constituents at multiple length scales. Although much is understood about the link between structure and function in many tissues, it is still unclear how complex tissue architectures are produced by collections of cells, especially when one considers that tissue patterning occurs over length scales much larger than that of the single cell. A key observation is that cells can communicate through the long range transmission of forces, which in turn implies that the shape of the physical environment may influence cell behaviour and thus tissue patterning. Inspired by the topology of trabecular bone, we have developed an in-vitro experimental system which enables us to explore how bone-like cells respond to constant mean- and negative Gaussian- curvature surfaces. We find that the macroscopic shape of tissues growing on these surfaces can be described by the Laplace-Young equation and furthermore demonstrate the importance of mean surface curvature on the local rate of tissue growth. A surprising outcome is that after sufficient growth, the tissues self-organise into long range chiral structures, in many ways similar to the twisting arrangement of collagen that is found around osteons in bone. Despite the relative simplicity of these surfaces, they give rise to a rich cell and tissue behaviour that helps us understand more about the fundamentals of tissue morphogenesis, thus inspiring the design of new materials for regenerative medicine.