The structure of the [001]-oriented single crystalline tungsten probes sharpened in ultra-high vacuum using electron beam heating and ion sputtering has been studied using scanning and transmission electron microscopy. The electron microscopy data prove reproducible fabrication of the single-apex tips with nanoscale pyramids grained by the {011} planes at the apexes. These sharp, [001]-oriented tungsten tips have been successfully utilized in high resolution scanning tunneling microscopy imaging of HOPG(0001), SiC(001) and graphene/SiC(001) surfaces. The electron microscopy characterization performed before and after the high resolution STM experiments provides direct correlation between the tip structure and picoscale spatial resolution achieved in the experiments.