The technology is a DNA nanostructure of a defined geometric shape—a polyhedron or 6-helix bundle—with two to 100 antigen copies bound to its surface. The number of copies, the distance between them, their location on the nanostructure, and other physical features serve to improve the immune response triggered by the antigen compared to a control nucleic acid nanostructure containing at least one identical antigen copy. For HIV vaccines, the antigen is an HIV envelope glycoprotein gp120 (gp120) epitope. The technology can also include one or more moieties, including adjuvants, targeting molecules, and therapeutic agents, as well as a coating for increased stabilization and protection. To enhance immune response, these nanostructures can incorporate multiple copies of an immunostimulatory agent such as a toll-like receptor (TLR) agonist. The physical design of these immunostimulatory agents, as well as their locations on the nanostructure, provide increased immunostimulation compared to a single immunostimulatory agent.