On the Equilibrium Shape of an Ice Crystal
  We examine the shape of a an isolated, dislocation-free ice crystal when it is in equilibrium with the vapor phase in an isothermal closed environment, as a function of temperature. From our analysis we draw the following conclusions: 1) The equilibrium shape has not yet been definitively measured for ice crystals; 2) The surface energy anisotropy is likely cusp-like near the facet angles, and the size of the cusps can be estimated from crystal growth measurements; 3) The equilibrium shape is likely nearly spherical with only small faceted regions; 4) The time needed to reach equilibrium is likely prohibitively long, except under special circumstances; and 5) Surface energy effects likely play a relatively smaller role in ice crystal growth dynamics when compared to the role of attachment kinetics. 
Kenneth G. Libbrecht
cond-mat.mtrl-sci