Crystallography Reports, Vol. 48, No. 3, 2003, pp. 347–350. Translated from Kristallografiya, Vol. 48, No. 3, 2003, pp. 391–394. Original Russian Text Copyright © 2003 by Talis. THEORY OF CRYSTAL STRUCTURES Structural Characteristics of Gas Hydrates within the Framework of Generalized Crystallography A. L. Talis Russian Institute of Synthesis of Mineral Raw Materials, Aleksandrov, Vladimir oblast, 601650 Russia e-mail:
[email protected] Received September 16, 2002 Abstract—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 relation- ships obtained may be considered as a basis for an a priori derivation of the determined (periodic and aperiodic) structures of gas hydrates. © 2003 MAIK “Nauka/Interperiodica”. The impossibility of dividing the three-dimensional pentagonal “cap” of the icosahedron into a hexagonal Euclidean space E3 into regular tetrahedra determines 2π one (if a wedge with an angle ------ is inserted), with the the structural characteristics of tetrahedrally coordi- 5 nated aqueous frameworks of gas hydrates that cannot disclination interactions being determined by the prod- be adequately reflected within the framework of classi- uct of the corresponding elements of group Y'. The cal crystallography. For example, the polyhedra–cavi- 2π introduction of two, three, and four Ð------ disclinations ties D, T, P, and H (dodecahedron, tetra-, penta-, and 5 hexadecahedra), the constituent fragments of the struc- into an icosahedron along its fivefold axes results in the tures of gas hydrates, are determined as dual to the Z12, formation of the Z14, Z15, and Z16 polyhedra [2].