  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.
