  Topological properties of crystalline ice structures are studied by
considering ring statistics, coordination sequences, and topological density of
different ice phases. The coordination sequences (number of sites at
topological distance k from a reference site) have been obtained by direct
enumeration until at least 40 coordination spheres for different ice
polymorphs. This allows us to study the asymptotic behavior of the mean number
of sites in the k-th shell, M_k, for high values of k: M_k ~ a k^2, a being a
structure-dependent parameter. Small departures from a strict parabolic
dependence have been studied by considering first and second differences of the
series {M_k} for each structure. The parameter a ranges from 2.00 for ice VI to
4.27 for ice XII, and is used to define a topological density for these solid
phases of water. Correlations between such topological density and the actual
volume of ice phases are discussed. Ices Ih and Ic are found to depart from the
general trend in this correlation due to the large void space in their
structures.
