[en] We investigate the three-dimensional morphology of the dendrite tip using the phase-field method. We find that, for low undercoolings, this morphology is ostensibly independent of anisotropy strength except for a localized shape distortion near the tip that only affects the value of the tip radius ρ [which is crudely approximated by ρ≅(1-α)ρ_Iv where ρ_Iv is the Ivantsov tip radius of an isothermal paraboloid with the same tip velocity and α is the stiffness anisotropy]. The universal tip shape, which excludes this distortion, is well fitted by the form z=-r²/2+A₄r⁴ cos 4φ where |z| is the distance from the tip and all lengths are scaled by ρ_Iv. This fit yields A₄ in the range 0.004-0.005 in good quantitative agreement with the existing tip morphology measurements in succinonitrile [LaCombe et al., Phys. Rev. E 52, 2778 (1995)], which are reanalyzed here and found to be consistent with a single cos 4φ mode nonaxisymmetric deviation from a paraboloid. Moreover, the fin shape away from the tip is well fitted by the power law z=-a|x|^5/3 with a≅0.68. Finally, the characterization of the operating state of the dendrite tip is revisited in the light of these results. (c) 2000 The American Physical Society