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. Virusesaccess more complex higher triangulation number icosahedral architecturesby breaking perfect point group symmetry3-9, but nature appears not to have explored similar symmetry breaking fortetrahedral or octahedral symmetries. Here we describe a general design strategy for building higher triangulation number architectures starting fromregular 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.
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