Questions about how quasicrystals might self-assemble have been raised ever since their discovery. Overlapping clusters have been used to describe quasicrystal structures; how might they be related to growth? For Tsai-type quasicrystals, a subcluster of the RTH cluster used for their description may perhaps occur in the liquid, similar to the icosahedral clusters that Frank proposed may exist in single-component liquids. If so, then two such subclusters coming together would produce the overlap region between two RTH clusters, and the addition of a third subcluster would provide the combination of overlapping and face-to-face junctions that are seen in all of the Tsai-type quasicrystals and their periodic approximants. Stoichiometry alone would then determine whether the crystal growing around this large nucleus would be periodic or quasiperiodic.