We give a complete classification of Z_N orbifold compactification of the
heterotic SO(32) string theory and show its potential for realistic model
building. The appearance of spinor representations of SO(2n) groups is analyzed
in detail. We conclude that the heterotic SO(32) string constitutes an
interesting part of the string landscape both in view of model constructions
and the question of heterotic-type I duality.Comment: 21 pages, 5 figure