Fig. 1: Overview of the design strategy.

a–c, General design route to T = 4 icosahedral cages using substructures extracted from a T = 1 cage. Twelve pentagonal substructures (pentons) from a T = 1 cage (a) are docked with 20 homotrimers to form a closed cage structure (b), which creates hexagonal local structures (shaded red) placed between pentons (shaded yellow; c). d–f, Schematic of the route to T = 4 tetrahedral (d), octahedral (e) and icosahedral (f) cages. Step 1: T = 1 cages are designed starting from C3 symmetric trimeric building blocks. Step 2: the trimers constituting each face of the T = 1 cages are displaced away from the origin along the symmetry axis orthogonal to the face (left) and replaced by ABC-type pseudosymmetric heterotrimers to produce crowns in which one of the three components (yellow) is free to be designed to dock to other building blocks (right). Step 3: the crowns are docked with a new set of homotrimers aligned along the threefold symmetry axis of each architecture, which produces T = 4 cages.