Simulations of crystal growth from the melt are performed, using the Lennard-Jones potential. Growth of the (100), (111), and (110) faces of the fcc crystal from its melt are simulated. The measured growth rates show that the kinetic coefficient of the (100) face is about twice as high as that of the (111) and (110) faces, which have comparable kinetic coefficients. In order to perform measurements of the interface structure during growth, an order parameter is defined that discriminates between solid and liquid like particles on the basis of the symmetry properties of the local environment. The measurements show that the interface width for the three orientations is similar and does not increase appreciably with undercooling. The difference in occupation fraction in the layers in the interfacial region explains the larger kinetic coefficient found for the (100) face.