  We investigate the structural similarities between liquid water and 53 ices,
including 20 knowncrystalline phases. We base such similarity comparison on the
local environments that consist of atoms within a certain cutoff radius of a
central atom. We reveal that liquid water explores the localenvironments of the
diverse ice phases, by directly comparing the environments in these phases
using general atomic descriptors, and also by demonstrating that a
machine-learning potential trained on liquid water alone can predict the
densities, the lattice energies, and vibrational properties of theices. The
finding that the local environments characterising the different ice phases are
found in water sheds light on water phase behaviors, and rationalizes the
transferability of water models between different phases.
