In this paper we report the synthesis of colloidal CdSe/CdS core-shell heteronanoplatelets with epitaxially grown wurtzite (WZ) 1D CdS branches or legs by using cadmium diethyldithiocarbamate as a single-source precursor. The growth of WZ branches was achieved by exploiting zinc blende-wurtzite polytypism of cadmium chalcogenides induced by oleylamine. Synthesized 'nanospiders' exhibit enhanced absorption in the UV-blue region and narrow and relatively intense red photoluminescence depending on the amount of CdS in the heteronanostructure.