Classification of symmetric toroidal orbifolds.

We provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield N>=1 supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six dimensions. We find in total 520 inequivalent toroidal orbifolds, 162 of them with Abelian point groups such as Z_3, Z_4, Z_6-I etc. and 358 with non-Abelian point groups such as S_3, D_4, A_4 etc. We also briefly explore the properties of some orbifolds with Abelian point groups and N=1, i.e. specify the Hodge numbers and comment on the possible mechanisms (local or non-local) of gauge symmetry breaking.Comment: 51 pages, 24 figure