Structural characteristics of gas hydrates within the framework of generalized crystallography

It is shown that the symmetry of the {5, 3, 3} polytope (four-dimensional dodecahedron) embedded into E4 enables one to derive all the polyhedra—cavities that make up gas hydrates from the {5, 3} dodecahedron. Consideration is given to the allomorphic embedding of the {5, 3} subgraph into the incidence graph of the Desargues configuration 103, which determines the mechanism of incorporation of guest molecules into the polyhedra—cavities of gas hydrates and their escape from these polyhedra at the symmetry level. The relationships obtained may be considered as a basis for an a priori derivation of the determined (periodic and aperiodic) structures of gas hydrates.