  The self-assembly of colloidal diamond (CD) crystals is considered as one of
the most coveted goals of nanotechnology, both from the technological and
fundamental points of view. For applications, colloidal diamond is a photonic
crystal which can open new possibilities of manipulating light for information
processing. From a fundamental point of view, its unique symmetry exacerbates a
series of problems that are commonly faced during the self-assembly of target
structures, such as the presence of kinetic traps and the formation of
crystalline defects and alternative structures (polymorphs). Here we
demonstrate that all these problems can be systematically addressed via
SAT-assembly, a design framework that converts self-assembly into a
satisfiability problem. Contrary to previous solutions (requiring four or more
components), we prove that the assembly of the CD crystal only requires a
binary mixture. Moreover, we use molecular dynamics simulations of a system
composed by nearly a million nucleotides to test a DNA nanotechnology design
that constitutes a promising candidate for experimental realization.
