Multivalent presentation of viral glycoproteins can substantially increase the elicitation of antigen-specific antibodies. To enable a new generation of anti-viral vaccines, we designed self-assembling protein nanoparticles with geometries tailored to present the ectodomains of influenza, HIV, and RSV viral glycoprotein trimers. We first de novo designed trimers tailored for antigen fusion, featuring N-terminal helices positioned to match the C termini of the viral glycoproteins. Trimers that experimentally adopted their designed configurations were incorporated as components of tetrahedral, octahedral, and icosahedral nanoparticles, which were characterized by cryo-electron microscopy and assessed for their ability to present viral glycoproteins. Electron microscopy and antibody binding experiments demonstrated that the designed nanoparticles presented antigenically intact prefusion HIV-1 Env, influenza hemagglutinin, and RSV F trimers in the predicted geometries. This work demonstrates that antigen-displaying protein nanoparticles can be designed from scratch, and provides a systematic way to investigate the influence of antigen presentation geometry on the immune response to vaccination.