Abstract: We provide a general and modular solution for building synthetic icosahedral shells on the scale of 100 nm, motivated by the 1962 Caspar and Klug theory of virus structure. Strategies were explored for controlling the pathways, kinetics, and the yield by which subunits arrange themselves into icosahedral symmetry. The methods of DNA origami were employed to produce accurately-designed and rigid building blocks. We created multiple large virus-like capsids and validated the structures using cryo electron microscopy and studied the capsid assembly process experimentally and with a computational model to elucidate how the kinetics and yield of target structures depends on control parameters. Our capsid building blocks represent a near-ideal manifestation of patchy particles whose geometry and interactions can be designed with sub-nanometer and kBT precision, thus achieving a long sought after goal in soft matter physics. Applications range from drug delivery to a generalized antiviral agent, which is demonstrated for hepatitis B.