Nanoscale materials are currently being exploited as active components in a wide range of technological applications in various fields, such as composite materials(1,2), chemical sensing(3), biomedicine(4-6), optoelectronics(7-9) and nanoelectronics(10-12). Colloidal nanocrystals are promising candidates in these fields, due to their ease of fabrication and processibility. Even more applications and new functional materials might emerge if nanocrystals could be synthesized in shapes of higher complexity than the ones produced by current methods (spheres, rods, discs)(13-19). Here, we demonstrate that polytypism, or the existence of two or more crystal structures in different domains of the same crystal, coupled with the manipulation of surface energy at the nanoscale, can be exploited to produce branched inorganic nanostructures controllably. For the case of CdTe, we designed a high yield, reproducible synthesis of soluble, tetrapod-shaped nanocrystals through which we can independently control the width and length of the four arms.