Classification of 1D and 2D Orbifolds

In these proceedings we present a complete classification of all one- and two-dimensional orbifold compactifications. Our study is based on the classification of crystallographic space groups. There exist two 1D and seventeen 2D orbifolds. Many of them have so far not been considered for the compactification of higher-dimensional string or quantum field theories. We determine the most general parities for each of the orbifolds and construct the corresponding basis functions.