Colloidal core/shell nanocrystals are key materials for optoelectronics, enabling control over essential properties via precise engineering of the shape, thickness, and crystal lattice structure of their shell. Here, we apply the growth protocol for CdS branched nanocrystals on CdSe nanoplatelet seeds and obtain bone-shaped heterostructures with a highly anisotropic shell. Surprisingly, the nanoplatelets withstand the high growth temperature of 350 {deg}C and we obtain structures with a CdSe nanoplatelet core that is overcoated by a shell of cubic CdS, on top of which tetrahedral CdS structures with hexagonal lattice are formed. These complex core/shell nanocrystals show a bandedge emission around 657 nm with a photoluminescence quantum yield of ca. 42 % in solution, which is also retained in thin films. Interestingly, the nanocrystals manifest simultaneous red and green emission, and the relatively long wavelength of the green emission indicates charge recombination at the cubic/hexagonal interface of the CdS shell. The nanocrystal films show amplified spontaneous emission, random lasing, and distributed feedback lasing when the material is deposited on suitable gratings. Our work stimulates the design and fabrication of more exotic core/shell heterostructures where charge carrier delocalization, dipole moment, and other optical and electrical properties can be engineered.