Cytokinesis in many eukaryotic cells is orchestrated by a contractile actomyosin ring. While many of the proteins involved are known, the mechanism of constriction remains unclear. Informed by the existing literature and new three-dimensional (3D) molecular details from electron cryotomography, here we develop 3D coarse-grained models of actin filaments, unipolar and bipolar myosins, actin cross-linkers, and membranes and simulate their interactions. Assuming that local force on the membrane results in inward growth of the cell wall, we explored a matrix of possible actomyosin configurations and found that node-based architectures like those presently described for ring assembly result in membrane puckers not seen in electron microscope images of real cells. Instead, the model that best matches data from fluorescence microscopy, electron cryotomography, and biochemical experiments is one in which actin filaments transmit force to the membrane through evenly distributed, membrane-attached, unipolar myosins, with bipolar myosins in the ring driving contraction. While at this point this model is only favored (not proven), the work highlights the power of coarse-grained biophysical simulations to compare complex mechanistic hypotheses.