Studies of crystal growth kinetics are tightly integrated with advances in the creation of new nanoscale inorganic building blocks and their functional assemblies 1-11. Recent examples include the development of semiconductor nanorods which have potential uses in solar cells 12-17, and the discovery of a light driven process to create noble metal particles with sharp corners that can be used in plasmonics 18,19. In the course of studying basic crystal growth kinetics we developed a process for preparing branched semiconductor nanocrystals such as tetrapods and inorganic dendrimers of precisely controlled generation 20,21. Here we report the discovery of a crystal growth kinetics regime in which a new class of hyper-branched nanocrystals are formed. The shapes range from 'thorny balls', to tree-like ramified structures, to delicate 'spider net'-like particles. These intricate shapes depend crucially on a delicate balance of branching and extension. The multitudes of resulting shapes recall the diverse shapes of snowflakes22. The three dimensional nature of the branch points here, however, lead to even more complex arrangements than the two dimensionally branched structures observed in ice. These hyper-branched particles not only extend the available three-dimensional shapes in nanoparticle synthesis, but also provide a tool to study growth kinetics by carefully observing and modeling particle morphology.