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Icosahedral capsids are ubiquitous among spherical viruses, yet their assem- bly pathways and governing interactions remain elusive. We present a molecular dynamics model that incorporates essential physical and biological interactions, including protein diffusion, genome flexibility, and a conformational switch that mimics allostery and activates the elastic properties of proteins upon binding. This switch makes the simulations computationally feasible and enables the assembly of icosahedral capsids around a flexible genome—overcoming long-standing lim- itations in previous models. Using this framework, we successfully reproduce the self-assembly of subunits around a flexible genome into icosahedral shells with numbers greater than one – most notably 3, the most common structure in na- ture – a feat that rigid-body models have so far failed to achieve. We systematically explore the range of morphologies formed with different genome architectures, in line with in vitro experiments using cowpea chlorotic mottle virus capsid proteins: viral RNAs with more complex structure form more complete and stable capsids than linear ones. These results provide a predictive framework for genome-guided assembly and capsid design.