A special class of simple 24-vertex polyhedra and tetrahedrally coordinated structures of gas hydrates

摘要

It is established that the eight-dimensional lattice E₈ and the Mathieu group M₁₂ 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.