We present a new microphysical model for the vapor growth and aspect ratio evolution of faceted, hexagonal ice crystals in the atmosphere. Our model is based on a novel, efficient numerical method for solving Laplace's equation for steady state diffusion on the surface of a three-dimensional hexagonal prism, and also takes into account the surface kinetic processes of crystal growth. We do not include ventilation, so our model is limited to stationary crystals or falling crystals smaller than 100 μm. We calculate a self-consistent solution for the distribution of the supersaturation and the condensation coefficient on each crystal face, for several different assumptions regarding the crystal growth mechanism and ice surface properties. We use this model to predict the aspect ratios expected for faceted ice crystals over a range of temperatures and supersaturations, as well as to estimate the conditions for which faceted growth becomes unstable and the crystals become hollowed or dendritic. We compare these predictions to observed features of ice cloud crystals to infer some microphysical characteristics of ice crystals and their temperature dependence. We also compare our predicted mass growth rates with those of the capacitance model for spheres and ellipsoids to look at the effects of shape and surface kinetics. Finally, we insert the single-particle code into a simple parcel cloud model to investigate the feedbacks between crystal surface kinetics, shape, and the thermodynamic properties of clouds. ¿ 2001 American Geophysical Union