Equilibrium Wulff shapes and interfacial energies of two-dimensional "crystals" on a triangular lattice are considered. Asymptotic approximations are constructed for both the shapes and energies in the limit T-->0 where crystals are close to perfect hexagons, and the limit T-T-c. (critical temperature) where crystals have near-circular shapes. The intermediate temperature region is studied numerically, and accurate interpolating approximations are proposed. The relevance of the study to the nucleation problem is discussed.