Structure of ice Ih and ice Ic as described in the language of Delaunay simplices

Classification of the Delaunay simplex forms is carried out for the ideal structures of ice Ih and ice Ic. Classification according to the number of edges of different length reveals six types of simplices, while classification according to the number and mutual positions of edges of the unit length (equal to the length of the hydrogen bond) reveals five types of indices. Ice Ic is composed of simplices of three types (one of which has the form of a perfect tetrahedron), ice Ih from six simplices. Degeneracy is removed in computer models of slightly distorted ice by means of insignificant shifting of water molecules from their ideal positions. This makes it possible to provide the unambiguous partition of the crystal structure into Delaunay simplices. It is found that degeneracy removal results in the appearance of Delaunay simplices of specific forms with a very small volume (Kije simplices). The shape characteristics of simplices of different types and their percentage are calculated in the large computer models of ice. In particular, the fraction of the Kije simplices is found to be about 7.5% in ice Ih.