Abstract AlphaFold can predict the structures of monomeric and multimeric proteins with high accuracy but has a limit on the number of chains and residues it can fold. Here we show that a combination of AlphaFold and all-atom symmetric docking simulations enables highly accurate prediction of the structure of complex symmetrical assemblies. We present a method to predict the structure of complexes with cubic – tetrahedral, octahedral and icosahedral – symmetry from sequence. Focusing on proteins where AlphaFold can make confident predictions on the subunit structure, 27 cubic systems were assembled with a median TM-score of 0.99 and a DockQ score of 0.72. 21 had TM-scores of above 0.9 and were categorized as acceptable- to high-quality according to DockQ. The resulting models are energetically optimized and can be used for detailed studies of intermolecular interactions in higher-order symmetrical assemblies. The results demonstrate how explicit treatment of structural symmetry can significantly expand the size and complexity of AlphaFold predictions.