  Molecular simulations of the self-assembly of cone-shaped particles with
specific, attractive interactions are performed. Upon cooling from random
initial conditions, we find that the cones self assemble into clusters and that
clusters comprised of particular numbers of cones (e.g. 4 - 17, 20, 27, 32, 42)
have a unique and precisely packed structure that is robust over a range of
cone angles. These precise clusters form a sequence of structures at specific
cluster sizes- a precise packing sequence - that for small sizes is identical
to that observed in evaporation-driven assembly of colloidal spheres. We
further show that this sequence is reproduced and extended in simulations of
two simple models of spheres self-assembling from random initial conditions
subject to certain convexity constraints. This sequence contains six of the
most common virus capsid structures obtained in vivo including large chiral
clusters, and a cluster that may correspond to several non-icosahedral,
spherical virus capsid structures obtained in vivo. Our findings suggest this
precise packing sequence results from free energy minimization subject to
convexity constraints and is applicable to a broad range of assembly processes.
