  The control over the self-assembly of complex structures is a long-standing
challenge of material science, especially at the colloidal scale, as the
desired assembly pathway is often kinetically derailed by the formation of
amorphous aggregates. Here we investigate in detail the problem of the
self-assembly of the three Archimedean shells with five contact points per
vertex, i.e. the icosahedron, the snub cube, and the snub dodecahedron. We use
patchy particles with five interaction sites (or patches) as model for the
building blocks, and recast the assembly problem as a Boolean satisfiability
problem (SAT) for the patch-patch interactions. This allows us to find
effective designs for all targets, and to selectively suppress unwanted
structures. By tuning the geometrical arrangement and the specific interactions
of the patches, we demonstrate that lowering the symmetry of the building
blocks reduces the number of competing structures, which in turn can
considerably increase the yield of the target structure. These results cement
SAT-assembly as an invaluable tool to solve inverse design problems.
