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A previously proposed Monte Carlo model (Xiao et al., 1988, 1990) is extended to three dimensions, and reevaporation after accommodation and growth on dislocation-induced steps are included. It is found again that, for a given set of growth parameters, the critical size beyond which a crystal cannot retain its macroscopically faceted shape scales linearly with the mean free path in the vapor. However, the three-dimensional systems show increased shape stability as compared with the corresponding two-dimensional cases. The experimental observation that the critical size of a growing crystal depends on the prevailing growth mechanism is confirmed, and detailed insight into the processes leading to the loss of face and facet stability is obtained.