Growth-melt asymmetry in crystals and twelve-sided snowflakes

It is in the lexicon of crystal growth that the shape of a growing crystal reflects the underlying microscopic architecture. Although it is known that in weakly nonequilibrium conditions the slowest growing orientations ultimately dominate the asymptotic shape, is the same true for melting? Here we observe and show theoretically that while the two-dimensional steady melt shapes of ice are bounded by six planes, these planes are not proper facets but instead are rotated 30 degrees from the prism planes of ice. Finally, the transient melting state exposes 12 apparent crystallographic planes thereby differing substantially from the transient growth state.