A special class of simple 24-vertex polyhedra and tetrahedrally coordinated structures of gas hydrates.
It is established that the eight-dimensional lattice E(8) and the Mathieu group M(12) determine a unique sequence of algebraic geometry constructions which define a special class of simple 24-vertex, 14-face polyhedra with four-, five- and six-edge faces. As an example, the graphs of the ten stereohedra that generate most known tetrahedrally coordinated water cages of gas hydrates have been derived a priori. A structural model is proposed for the phase transition between gas hydrate I and ice.
Samoylovich
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Central Research and Technology Institute TechnoMash, Moscow. samoylovich@technomash.ru
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