  We derive a phase diagram for amorphous solids and liquid supercooled water
and explain why the amorphous solids of water exist in several different forms.
Application of large-deviation theory allows us to prepare such phases in
computer simulations. Along with nonequilibrium transitions between the ergodic
liquid and two distinct amorphous solids, we establish coexistence between
these two amorphous solids. The phase diagram we predict includes a
nonequilibrium triple point where two amorphous phases and the liquid coexist.
While the amorphous solids are long-lived and slowly-aging glasses, their
melting can lead quickly to the formation of crystalline ice. Further, melting
of the higher density amorphous solid at low pressures takes place in steps,
transitioning to the lower density glass before accessing a nonequilibrium
liquid from which ice coarsens.
