Ricci-flat compactifications in superstring theory and Coxeter automorphisms. I

A class of vacuum configurations in superstring theory in the case of compactification from ten to four dimensions is constructed. The configurations are obtained by factorizing tori of semisimple Lie groups with respect to finite symmetry groups. A complete list of the configurations obtained by applying Coxeter transformations is given. Some topological characteristics having a phenomenological significance are calculated.