Actin filament networks play an active role in cytokinesis of eukaryotic cells. These networks, linked mainly by myosin, are concentrated below the cell membrane forming a spherical supporting shell. During cytokinesis, this network is modified such that a contractile ring is formed along the diameter of the shell. We present a realistic three-dimensional simulation model to study the dynamics of this spherical shell of elastic actin filaments and myosin motors. The results show compelling evidence that this fibre-spring model, with the motors activated in a narrow region around the division plane, is sufficient to reproduce most of the essential mechanics of cytokinesis: A spontaneous formation of a contractile ring, a characteristic filament orientation structure, and realistic cleavage furrow dynamics. These results demonstrate that, though cytokinesis is a highly complex process with large variation in intricate details, the fundamental dynamics are largely generic. In particular, motor mediated contraction of an unstructured filament mesh is sufficient to undergo division without concentrated and directed polymerization in the cleavage zone.