Scanning tunneling microscopy (STM) has been used to image the equilibrium shape of small 2d and 3d crystallites supported on single crystal substrates. Due to the high resolution of STM, highly accurate shape information is obtained. Concerning 3d particles, special attention was given to the step structure of facets and the curved portions near facets. The shape of the (111) facet of Pb particles, prepared and equilibrated on Cu(111) under ultrahigh vacuum conditions, exhibits a threefold symmetry. The facet edge can be determined with atomic resolution. Hence an accurate analysis of the Pb equilibrium crystal shape (ECS) near facets is possible yielding shape exponents. Expected universal exponents of 3/2 or 2 are not found. Instead, shape exponents exhibit an azimuthal dependence, with values ranging between 1.4 and 1.7. This variation, consistent with the threefold symmetry of the (111) facet, suggests a structure dependent step interaction behavior and, furthermore, that the facet to vicinal surface transition does not belong to the Pokrovsky-Talapov universality class. By comparison, the ECS of 2d islands on Pb(111) is also threefold symmetric and yields orientation dependent relative step energies. Thus, the data of 2d Pb islands on Pb(111) supplement those obtained from the (111) facet of the ECS of 3d Pb particles.