Four, eight or twenty C3 symmetric protein trimers can be arranged with tetrahedral, octahedral or icosahedral point group symmetry to generate closed cage-like structures1,2. Viruses access more complex higher triangulation number icosahedral architectures by breaking perfect point group symmetry3–9, but nature appears not to have explored similar symmetry breaking for tetrahedral or octahedral symmetries. Here we describe a general design strategy for building higher triangulation number architectures starting from regular polyhedra through pseudosymmetrization of trimeric building blocks. Electron microscopy confirms the structures of T = 4 cages with 48 (tetrahedral), 96 (octahedral) and 240 (icosahedral) subunits, each with 4 distinct chains and 6 different protein–protein interfaces, and diameters of 33 nm, 43 nm and 75 nm, respectively. Higher triangulation number viruses possess very sophisticated functionalities; our general route to higher triangulation number nanocages should similarly enable a next generation of multiple antigen-displaying vaccine candidates10,11 and targeted delivery vehicles12,13.
